diff --git a/CHANGES.md b/CHANGES.md
index 682500d..a56980b 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -2,6 +2,7 @@
 
 ## Version 0.4.0 (in development)
 
+- Fixed and enhanced core rule `time-coordinate`. `(#33)
 - New xcube rule `no-chunked-coords`. (#29)
 - New xcube multi-level dataset rules:
   - `ml-dataset-meta`: verifies that a meta info file exists and is consistent;
diff --git a/docs/rule-ref.md b/docs/rule-ref.md
index 9cb8076..7c1c488 100644
--- a/docs/rule-ref.md
+++ b/docs/rule-ref.md
@@ -59,7 +59,7 @@ Contained in:  `all`-:material-lightning-bolt: `recommended`-:material-alert:
 
 ### :material-bug: `time-coordinate`
 
-Time coordinate (standard_name='time') should have unambiguous time units encoding.
+Time coordinates should have valid and unambiguous time units encoding.
 [:material-information-variant:](https://cfconventions.org/cf-conventions/cf-conventions.html#time-coordinate)
 
 Contained in:  `all`-:material-lightning-bolt: `recommended`-:material-lightning-bolt:
diff --git a/tests/plugins/core/rules/test_time_coordinate.py b/tests/plugins/core/rules/test_time_coordinate.py
index f917f9f..3c56de4 100644
--- a/tests/plugins/core/rules/test_time_coordinate.py
+++ b/tests/plugins/core/rules/test_time_coordinate.py
@@ -12,7 +12,6 @@
             dims="time",
             attrs={
                 "standard_name": "time",
-                "long_name": "time",
             },
         ),
     },
@@ -27,36 +26,70 @@
 valid_dataset_2 = valid_dataset_1.copy()
 del valid_dataset_2.time.encoding["units"]
 del valid_dataset_2.time.encoding["calendar"]
-valid_dataset_2.time.attrs["units"] = "seconds since 2000-01-01 UTC"
+valid_dataset_2.time.attrs["units"] = "seconds since 2000-1-1 +2:00"
 valid_dataset_2.time.attrs["calendar"] = "gregorian"
 
 # OK, because not identified as time
 valid_dataset_3 = valid_dataset_1.copy()
+del valid_dataset_3.time.encoding["units"]
 del valid_dataset_3.time.attrs["standard_name"]
 
-# OK, because we only look for standard_name
+# OK, because we only look for time units
 valid_dataset_4 = valid_dataset_1.rename_vars({"time": "tm"})
+del valid_dataset_4.tm.attrs["standard_name"]
 
-# Invalid, because long_name is missing
+# OK, because not recognized as time coord
+valid_dataset_5 = valid_dataset_1.copy()
+valid_dataset_5.time.encoding["units"] = 1
+del valid_dataset_5.time.attrs["standard_name"]
+
+# Invalid, because units is invalid but standard_name given
 invalid_dataset_0 = valid_dataset_1.copy()
-del invalid_dataset_0.time.attrs["long_name"]
+invalid_dataset_0.time.encoding["units"] = 1
 
-# Invalid, because we require units
+# Invalid, because we require units but standard_name given
 invalid_dataset_1 = valid_dataset_1.copy(deep=True)
 del invalid_dataset_1.time.encoding["units"]
 
-# Invalid, because we require calendar
+# Invalid, because we no time units although standard_name given
 invalid_dataset_2 = valid_dataset_1.copy(deep=True)
-del invalid_dataset_2.time.encoding["calendar"]
+invalid_dataset_2.time.encoding["units"] = "years from 2000-1-1 +0:0"
 
-# Invalid, because we require TZ units part
+# Invalid, because we require calendar
 invalid_dataset_3 = valid_dataset_1.copy(deep=True)
-invalid_dataset_3.time.encoding["units"] = "seconds since 2000-01-01 00:00:00"
+del invalid_dataset_3.time.encoding["calendar"]
 
-# Invalid, because we require units format wrong
+# Invalid, because we use invalid UOT
 invalid_dataset_4 = valid_dataset_1.copy(deep=True)
-invalid_dataset_4.time.encoding["units"] = "2000-01-01 00:00:00 UTC"
+invalid_dataset_4.time.encoding["units"] = "millis since 2000-1-1 +0:0"
+
+# Invalid, because we use ambiguous UOT
+invalid_dataset_5 = valid_dataset_1.copy(deep=True)
+invalid_dataset_5.time.encoding["units"] = "years since 2000-1-1 +0:0"
+
+# Invalid, because we require timezone
+invalid_dataset_6 = valid_dataset_1.copy(deep=True)
+invalid_dataset_6.time.encoding["units"] = "seconds since 2000-01-01 00:00:00"
+
+# Invalid, because we require timezone
+invalid_dataset_7 = valid_dataset_1.copy(deep=True)
+invalid_dataset_7.time.encoding["units"] = "seconds since 2000-01-01"
+
+# Invalid, because we have 6 units parts
+invalid_dataset_8 = valid_dataset_1.copy(deep=True)
+invalid_dataset_8.time.encoding["units"] = "days since 2000-01-01 12:00:00 +0:00 utc"
+
+# Invalid, because we date part is invalid
+invalid_dataset_9 = valid_dataset_1.copy(deep=True)
+invalid_dataset_9.time.encoding["units"] = "days since 00-01-01 12:00:00 +0:00"
+
+# Invalid, because we time part is invalid
+invalid_dataset_10 = valid_dataset_1.copy(deep=True)
+invalid_dataset_10.time.encoding["units"] = "days since 2000-01-01 12:00 +0:00"
 
+# Invalid, because we tz part is invalid
+invalid_dataset_11 = valid_dataset_1.copy(deep=True)
+invalid_dataset_11.time.encoding["units"] = "days since 2000-01-01 12:00:00 utc"
 
 TimeCoordinateTest = RuleTester.define_test(
     "time-coordinate",
@@ -67,6 +100,7 @@
         RuleTest(dataset=valid_dataset_2),
         RuleTest(dataset=valid_dataset_3),
         RuleTest(dataset=valid_dataset_4),
+        RuleTest(dataset=valid_dataset_5),
     ],
     invalid=[
         RuleTest(dataset=invalid_dataset_0),
@@ -74,5 +108,12 @@
         RuleTest(dataset=invalid_dataset_2),
         RuleTest(dataset=invalid_dataset_3),
         RuleTest(dataset=invalid_dataset_4),
+        RuleTest(dataset=invalid_dataset_5),
+        RuleTest(dataset=invalid_dataset_6),
+        RuleTest(dataset=invalid_dataset_7),
+        RuleTest(dataset=invalid_dataset_8),
+        RuleTest(dataset=invalid_dataset_9),
+        RuleTest(dataset=invalid_dataset_10),
+        RuleTest(dataset=invalid_dataset_11),
     ],
 )
diff --git a/xrlint/plugins/core/rules/time_coordinate.py b/xrlint/plugins/core/rules/time_coordinate.py
index 7699d55..e830437 100644
--- a/xrlint/plugins/core/rules/time_coordinate.py
+++ b/xrlint/plugins/core/rules/time_coordinate.py
@@ -1,9 +1,45 @@
+import re
+
+
 from xrlint.node import DataArrayNode
 from xrlint.plugins.core.plugin import plugin
 from xrlint.rule import RuleContext, RuleOp
 
 
-_EXPECTED_UNITY_FORMAT = "<unit> since <date> <time> <timezone>"
+_EXAMPLE_UNIT_1 = "seconds since 2010-10-8 15:15:42.5 -6:00"
+_EXAMPLE_UNIT_2 = "days since 2000-01-01 +0:00"
+
+_AMBIGUOUS_UNITS_OF_TIME = (
+    "years",
+    "year",
+    "y",
+    "months",
+    "month",
+    "m",
+)
+
+_UNAMBIGUOUS_UNITS_OF_TIME = (
+    "days",
+    "day",
+    "d",
+    "hours",
+    "hour",
+    "hr",
+    "h",
+    "minutes",
+    "minute",
+    "min",
+    "seconds",
+    "second",
+    "sec",
+    "s",
+)
+
+_ALL_UNITS_OF_TIME = (*_AMBIGUOUS_UNITS_OF_TIME, *_UNAMBIGUOUS_UNITS_OF_TIME)
+
+_RE_DATE = re.compile(r"^\d{4}-\d{1,2}-\d{1,2}$")
+_RE_TIME = re.compile(r"^\d{1,2}:\d{1,2}:\d{1,2}(\.\d{1,6})?$")
+_RE_TZ = re.compile(r"^[+-]\d{1,2}:\d{1,2}$")
 
 
 @plugin.define_rule(
@@ -11,8 +47,7 @@
     version="1.0.0",
     type="problem",
     description=(
-        "Time coordinate (standard_name='time') should have"
-        " unambiguous time units encoding."
+        "Time coordinates should have valid and unambiguous time units encoding."
     ),
     docs_url=(
         "https://cfconventions.org/cf-conventions/cf-conventions.html#time-coordinate"
@@ -24,50 +59,113 @@ def data_array(self, ctx: RuleContext, node: DataArrayNode):
         attrs = array.attrs
         encoding = array.encoding
 
-        if node.name not in ctx.dataset.coords or attrs.get("standard_name") != "time":
+        units: str | None = encoding.get("units", attrs.get("units"))
+        if units is None:
+            if _is_time_by_name(attrs):
+                ctx.report("Missing 'units' attribute for time coordinate.")
+            # No more to check w.o. time units
+            return
+        elif not isinstance(units, str):
+            if _is_time_by_name(attrs):
+                ctx.report(
+                    f"Invalid 'units' attribute for time coordinate,"
+                    f" expected type str, got {type(units).__name__}."
+                )
+            # No more to check w.o. time units
             return
 
-        if attrs.get("long_name") != "time":
-            ctx.report("Attribute 'long_name' should be 'time'.")
+        units_ok = True
+        units_parts = units.split(" ")
+        num_unit_parts = len(units_parts)
+        is_time_by_units = num_unit_parts >= 3 and units_parts[1] == "since"
+        if not is_time_by_units:
+            if not _is_time_by_name(attrs):
+                # Not a time coordinate
+                return
+            units_ok = False
+        else:
+            # We have time units
 
-        use_units_format_msg = (
-            f"Specify 'units' attribute using format {_EXPECTED_UNITY_FORMAT!r}."
-        )
+            if not encoding.get("calendar", attrs.get("calendar")):
+                ctx.report(
+                    "Attribute/encoding 'calendar' should be specified.",
+                )
 
-        calendar: str | None = encoding.get("calendar", attrs.get("calendar"))
-        units: str | None = encoding.get("units", attrs.get("units"))
-        if not units or not calendar:
-            if not calendar:
+            uot_part = units_parts[0]
+            date_part = units_parts[2]
+            time_part = None
+            tz_part = None
+
+            if uot_part not in _ALL_UNITS_OF_TIME:
                 ctx.report(
-                    "Attribute 'calendar' should be specified.",
+                    f"Unrecognized units of measure for time"
+                    f" in 'units' attribute: {units!r}.",
+                    suggestions=[
+                        _units_format_suggestion(),
+                        _units_of_time_suggestion(),
+                    ],
                 )
-            if not units:
+            elif uot_part in _AMBIGUOUS_UNITS_OF_TIME:
                 ctx.report(
-                    "Attribute 'units' should be specified.",
-                    suggestions=[use_units_format_msg],
+                    f"Ambiguous units of measure for time in"
+                    f" 'units' attribute: {units!r}.",
+                    suggestions=[
+                        _units_format_suggestion(),
+                        _units_of_time_suggestion(),
+                    ],
                 )
-                # next checks concern units only
-                return
 
-        units_parts = units.split(" ")
-        # note, may use regex here
-        if len(units_parts) >= 4 and units_parts[1] == "since":
-            # format seems ok, check timezone part
-            last_part = units_parts[-1]
-            has_tz = last_part.lower() == "utc" or last_part[0] in ("+", "-")
-            if not has_tz:
+            if num_unit_parts == 3:
+                pass
+            elif num_unit_parts == 4:
+                time_or_tz_part = units_parts[3]
+                if _RE_TIME.match(time_or_tz_part):
+                    time_part = time_or_tz_part
+                else:
+                    tz_part = time_or_tz_part
+            elif num_unit_parts == 5:
+                time_part = units_parts[3]
+                tz_part = units_parts[4]
+            else:
+                time_part = units_parts[-2]
+                tz_part = units_parts[-1]
+                units_ok = False
+
+            if units_ok and not _RE_DATE.match(date_part):
+                units_ok = False
+            if units_ok and time_part and not _RE_TIME.match(time_part):
+                units_ok = False
+            if units_ok and tz_part and not _RE_TZ.match(tz_part):
+                units_ok = False
+
+            if not tz_part:
                 ctx.report(
-                    f"Missing timezone in 'units' attribute: {units!r}.",
+                    f"Missing timezone '+H:MM' or '-H:MM' in 'units' attribute: {units!r}.",
                     suggestions=[
-                        use_units_format_msg,
+                        _units_format_suggestion(),
                         f"Append timezone specification, e.g., use"
-                        f" {' '.join(units_parts[:-1] + ['utc'])!r}.",
+                        f" {' '.join(units_parts[:-1] + ['+0:00'])!r}.",
                     ],
                 )
-            # units ok
-            return
 
-        ctx.report(
-            f"Invalid 'units' attribute: {units!r}.",
-            suggestions=[use_units_format_msg],
-        )
+        if not units_ok:
+            ctx.report(
+                f"Invalid 'units' attribute: {units!r}.",
+                suggestions=[_units_format_suggestion()],
+            )
+
+
+def _units_format_suggestion():
+    use_units_format_msg = (
+        f"Specify 'units' attribute using the UDUNITS format,"
+        f" e.g., {_EXAMPLE_UNIT_1!r} or {_EXAMPLE_UNIT_2!r}."
+    )
+    return use_units_format_msg
+
+
+def _units_of_time_suggestion():
+    return f"Use one of {', '.join(map(repr, _UNAMBIGUOUS_UNITS_OF_TIME))}"
+
+
+def _is_time_by_name(attrs):
+    return attrs.get("standard_name") == "time" or attrs.get("axis") == "T"