diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index a6dbd626ec882f..19790ad4e6ff39 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -970,9 +970,8 @@ class Http2Session extends EventEmitter {
 
     const state = stream[kState];
     if (state.rst) {
-      // rst has already been called, do not call again,
-      // skip straight to destroy
-      stream.destroy();
+      // rst has already been called by self or peer,
+      // do not call again
       return;
     }
     state.rst = true;
diff --git a/test/parallel/test-http2-client-rststream-before-connect.js b/test/parallel/test-http2-client-rststream-before-connect.js
index 073b2d4837d2d2..3c4ac3b34d86ad 100644
--- a/test/parallel/test-http2-client-rststream-before-connect.js
+++ b/test/parallel/test-http2-client-rststream-before-connect.js
@@ -21,6 +21,10 @@ server.on('listening', common.mustCall(() => {
   // make sure that destroy is called
   req._destroy = common.mustCall(req._destroy.bind(req));
 
+  // second call doesn't do anything
+  assert.doesNotThrow(() => client.rstStream(req, 8));
+  assert.strictEqual(req.rstCode, 0);
+
   req.on('streamClosed', common.mustCall((code) => {
     assert.strictEqual(req.destroyed, true);
     assert.strictEqual(code, 0);