diff --git a/docs/project/changelog.rst b/docs/project/changelog.rst
index b7f4f62f9..de6b0be21 100644
--- a/docs/project/changelog.rst
+++ b/docs/project/changelog.rst
@@ -35,6 +35,10 @@ notice.
 Bug fixes
 .........
 
+* Fixed ``connection.recv(timeout=0)`` in the :mod:`threading` implementation.
+  If a message is already received, it is returned. Previously,
+  :exc:`TimeoutError` was raised incorrectly.
+
 * Wrapped errors when reading the opening handshake request or response in
   :exc:`~exceptions.InvalidMessage` so that :func:`~asyncio.client.connect`
   raises :exc:`~exceptions.InvalidHandshake` or a subclass when the opening
diff --git a/src/websockets/sync/messages.py b/src/websockets/sync/messages.py
index 98490797f..12e8b1623 100644
--- a/src/websockets/sync/messages.py
+++ b/src/websockets/sync/messages.py
@@ -79,7 +79,12 @@ def get_next_frame(self, timeout: float | None = None) -> Frame:
                 raise EOFError("stream of frames ended") from None
         else:
             try:
-                frame = self.frames.get(block=True, timeout=timeout)
+                # Check for a frame that's already received if timeout <= 0.
+                # SimpleQueue.get() doesn't support negative timeout values.
+                if timeout is not None and timeout <= 0:
+                    frame = self.frames.get(block=False)
+                else:
+                    frame = self.frames.get(block=True, timeout=timeout)
             except queue.Empty:
                 raise TimeoutError(f"timed out in {timeout:.1f}s") from None
         if frame is None:
@@ -143,7 +148,7 @@ def get(self, timeout: float | None = None, decode: bool | None = None) -> Data:
             deadline = Deadline(timeout)
 
             # First frame
-            frame = self.get_next_frame(deadline.timeout())
+            frame = self.get_next_frame(deadline.timeout(raise_if_elapsed=False))
             with self.mutex:
                 self.maybe_resume()
             assert frame.opcode is OP_TEXT or frame.opcode is OP_BINARY
@@ -154,7 +159,9 @@ def get(self, timeout: float | None = None, decode: bool | None = None) -> Data:
             # Following frames, for fragmented messages
             while not frame.fin:
                 try:
-                    frame = self.get_next_frame(deadline.timeout())
+                    frame = self.get_next_frame(
+                        deadline.timeout(raise_if_elapsed=False)
+                    )
                 except TimeoutError:
                     # Put frames already received back into the queue
                     # so that future calls to get() can return them.
diff --git a/tests/sync/test_messages.py b/tests/sync/test_messages.py
index d22693102..0a94b4f85 100644
--- a/tests/sync/test_messages.py
+++ b/tests/sync/test_messages.py
@@ -198,6 +198,12 @@ def test_get_timeout_after_first_frame(self):
         message = self.assembler.get()
         self.assertEqual(message, "café")
 
+    def test_get_if_received(self):
+        """get returns a text message if it's already received."""
+        self.assembler.put(Frame(OP_TEXT, b"caf\xc3\xa9"))
+        message = self.assembler.get(timeout=0)
+        self.assertEqual(message, "café")
+
     # Test get_iter
 
     def test_get_iter_text_message_already_received(self):