diff --git a/Lib/asyncio/streams.py b/Lib/asyncio/streams.py
index 0afc66a473..33fc303a6f 100644
--- a/Lib/asyncio/streams.py
+++ b/Lib/asyncio/streams.py
@@ -227,9 +227,6 @@ class StreamReaderProtocol(FlowControlMixin, protocols.Protocol):
             self._reject_connection = True
         self._stream_reader_wr = None
 
-    def _untrack_reader(self):
-        self._stream_reader_wr = None
-
     @property
     def _stream_reader(self):
         if self._stream_reader_wr is None:
@@ -345,9 +342,6 @@ class StreamWriter:
         return self._transport.can_write_eof()
 
     def close(self):
-        # a reader can be garbage collected
-        # after connection closing
-        self._protocol._untrack_reader()
         self._transport.close()
 
     def is_closing(self):
diff --git a/Lib/asyncio/subprocess.py b/Lib/asyncio/subprocess.py
index c86de3d087..90fc00de83 100644
--- a/Lib/asyncio/subprocess.py
+++ b/Lib/asyncio/subprocess.py
@@ -36,11 +36,6 @@ class SubprocessStreamProtocol(streams.FlowControlMixin,
             info.append(f'stderr={self.stderr!r}')
         return '<{}>'.format(' '.join(info))
 
-    def _untrack_reader(self):
-        # StreamWriter.close() expects the protocol
-        # to have this method defined.
-        pass
-
     def connection_made(self, transport):
         self._transport = transport
 
diff --git a/Lib/test/test_asyncio/test_streams.py b/Lib/test/test_asyncio/test_streams.py
index 0141df729c..740bb84c64 100644
--- a/Lib/test/test_asyncio/test_streams.py
+++ b/Lib/test/test_asyncio/test_streams.py
@@ -589,6 +589,7 @@ class StreamTests(test_utils.TestCase):
                 client_writer.write(data)
                 await client_writer.drain()
                 client_writer.close()
+                await client_writer.wait_closed()
 
             def start(self):
                 sock = socket.socket()
@@ -628,6 +629,7 @@ class StreamTests(test_utils.TestCase):
             # read it back
             msgback = await reader.readline()
             writer.close()
+            await writer.wait_closed()
             return msgback
 
         messages = []
@@ -666,6 +668,7 @@ class StreamTests(test_utils.TestCase):
                 client_writer.write(data)
                 await client_writer.drain()
                 client_writer.close()
+                await client_writer.wait_closed()
 
             def start(self):
                 self.server = self.loop.run_until_complete(
@@ -697,6 +700,7 @@ class StreamTests(test_utils.TestCase):
             # read it back
             msgback = await reader.readline()
             writer.close()
+            await writer.wait_closed()
             return msgback
 
         messages = []