diff --git a/Lib/subprocess.py b/Lib/subprocess.py
index 13600c28cf7117..f1d829a6f1724e 100644
--- a/Lib/subprocess.py
+++ b/Lib/subprocess.py
@@ -2061,7 +2061,11 @@ 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 aced87694cf7b6..3a63869231a3bd 100644
--- a/Lib/test/test_subprocess.py
+++ b/Lib/test/test_subprocess.py
@@ -3145,6 +3145,19 @@ 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)'],
diff --git a/Misc/NEWS.d/next/Library/2020-05-08-21-30-54.bpo-40550.i7GWkb.rst b/Misc/NEWS.d/next/Library/2020-05-08-21-30-54.bpo-40550.i7GWkb.rst
new file mode 100644
index 00000000000000..b0f3f03c34bbc5
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-05-08-21-30-54.bpo-40550.i7GWkb.rst
@@ -0,0 +1 @@
+Fix time-of-check/time-of-action issue in subprocess.Popen.send_signal.