diff --git a/Lib/socket.py b/Lib/socket.py
index db34ab37ee6..ed1b10a2549 100644
--- a/Lib/socket.py
+++ b/Lib/socket.py
@@ -193,7 +193,11 @@ class socket(_socket.socket):
         For IP sockets, the address info is a pair (hostaddr, port).
         """
         fd, addr = self._accept()
-        sock = socket(self.family, self.type, self.proto, fileno=fd)
+        # If our type has the SOCK_NONBLOCK flag, we shouldn't pass it onto the
+        # new socket. We do not currently allow passing SOCK_NONBLOCK to
+        # accept4, so the returned socket is always blocking.
+        type = self.type & ~globals().get("SOCK_NONBLOCK", 0)
+        sock = socket(self.family, type, self.proto, fileno=fd)
         # Issue #7995: if no default timeout is set and the listening
         # socket had a (non-zero) timeout, force the new socket in blocking
         # mode to override platform-specific socket flags inheritance.
diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index 17819f2fd17..63cc284eb36 100644
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -3866,6 +3866,7 @@ class NonBlockingTCPTests(ThreadedTCPSocketTest):
         read, write, err = select.select([self.serv], [], [])
         if self.serv in read:
             conn, addr = self.serv.accept()
+            self.assertIsNone(conn.gettimeout())
             conn.close()
         else:
             self.fail("Error trying to do accept after select.")
diff --git a/Misc/NEWS b/Misc/NEWS
index 6196671ba76..25845b06f39 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -190,6 +190,9 @@ Library
 - Issue #13248: Remove deprecated inspect.getargspec and inspect.getmoduleinfo
   functions.
 
+- Issue #25471: Sockets returned from accept() shouldn't appear to be
+  nonblocking.
+
 - Issue #25319: When threading.Event is reinitialized, the underlying condition
   should use a regular lock rather than a recursive lock.