diff --git a/Doc/library/asyncio-stream.rst b/Doc/library/asyncio-stream.rst
index e1568ae330b70f..05445219510ca5 100644
--- a/Doc/library/asyncio-stream.rst
+++ b/Doc/library/asyncio-stream.rst
@@ -316,13 +316,14 @@ StreamWriter
       If that fails, the data is queued in an internal write buffer until it can be
       sent.
 
+      The *data* buffer should be a bytes, bytearray, or C-contiguous one-dimensional
+      memoryview object.
+
       The method should be used along with the ``drain()`` method::
 
          stream.write(data)
          await stream.drain()
 
-      .. note::
-         The *data* buffer should be a C contiguous one-dimensional :term:`bytes-like object <bytes-like object>`.
 
    .. method:: writelines(data)
 
diff --git a/Lib/asyncio/selector_events.py b/Lib/asyncio/selector_events.py
index a7e27ccf0aa856..ff7e16df3c6273 100644
--- a/Lib/asyncio/selector_events.py
+++ b/Lib/asyncio/selector_events.py
@@ -1050,8 +1050,8 @@ def _read_ready__on_eof(self):
 
     def write(self, data):
         if not isinstance(data, (bytes, bytearray, memoryview)):
-            raise TypeError(f'data argument must be a bytes-like object, '
-                            f'not {type(data).__name__!r}')
+            raise TypeError(f'data argument must be a bytes, bytearray, or memoryview '
+                            f'object, not {type(data).__name__!r}')
         if self._eof:
             raise RuntimeError('Cannot call write() after write_eof()')
         if self._empty_waiter is not None: