diff --git a/Doc/library/threading.rst b/Doc/library/threading.rst
--- a/Doc/library/threading.rst
+++ b/Doc/library/threading.rst
@@ -804,8 +804,9 @@
       floating point number specifying a timeout for the operation in seconds
       (or fractions thereof).
 
-      This method returns the internal flag on exit, so it will always return
-      ``True`` except if a timeout is given and the operation times out.
+      This method returns true if and only if the internal flag has been set to
+      true by another thread, so it will always return ``True`` except if a
+      timeout is given and the operation times out.
 
       .. versionchanged:: 3.1
          Previously, the method always returned ``None``.
diff --git a/Lib/test/lock_tests.py b/Lib/test/lock_tests.py
--- a/Lib/test/lock_tests.py
+++ b/Lib/test/lock_tests.py
@@ -353,6 +353,22 @@
         for r, dt in results2:
             self.assertTrue(r)
 
+    def test_set_and_clear(self):
+        # Issue #13502: check that wait() returns true even when the event is
+        # cleared before the waiting thread is woken up.
+        evt = self.eventtype()
+        results = []
+        N = 5
+        def f():
+            results.append(evt.wait(1))
+        b = Bunch(f, N)
+        b.wait_for_started()
+        time.sleep(0.5)
+        evt.set()
+        evt.clear()
+        b.wait_for_finished()
+        self.assertEqual(results, [True] * N)
+
 
 class ConditionTests(BaseTestCase):
     """
diff --git a/Lib/threading.py b/Lib/threading.py
--- a/Lib/threading.py
+++ b/Lib/threading.py
@@ -408,9 +408,10 @@
     def wait(self, timeout=None):
         self._cond.acquire()
         try:
-            if not self._flag:
-                self._cond.wait(timeout)
-            return self._flag
+            signaled = self._flag
+            if not signaled:
+                signaled = self._cond.wait(timeout)
+            return signaled
         finally:
             self._cond.release()