diff --git a/Lib/subprocess.py b/Lib/subprocess.py
index 6a6c2fc..e259dc3 100644
--- a/Lib/subprocess.py
+++ b/Lib/subprocess.py
@@ -2078,7 +2078,11 @@ def send_signal(self, sig):
             # The race condition can still happen if the race condition
             # described above happens between the returncode test
             # and the kill() call.
-            os.kill(self.pid, sig)
+            try:
+                os.kill(self.pid, sig)
+            except ProcessLookupError:
+                # Supress the race condition error; bpo-40550.
+                pass
 
         def terminate(self):
             """Terminate the process with SIGTERM
diff --git a/Lib/test/test_subprocess.py b/Lib/test/test_subprocess.py
index e25474a..2a4c475 100644
--- a/Lib/test/test_subprocess.py
+++ b/Lib/test/test_subprocess.py
@@ -3229,6 +3229,19 @@ def test_send_signal_race(self):
         # so Popen failed to read it and uses a default returncode instead.
         self.assertIsNotNone(proc.returncode)
 
+    def test_send_signal_race2(self):
+        # bpo-40550: the process might exist between the returncode check and
+        # the kill operation
+        p = subprocess.Popen([sys.executable, '-c', 'exit(1)'])
+
+        # wait for process to exit
+        while not p.returncode:
+            p.poll()
+
+        with mock.patch.object(p, 'poll', new=lambda: None):
+            p.returncode = None
+            p.send_signal(signal.SIGTERM)
+
     def test_communicate_repeated_call_after_stdout_close(self):
         proc = subprocess.Popen([sys.executable, '-c',
                                  'import os, time; os.close(1), time.sleep(2)'],