diff --git a/requirements.txt b/requirements.txt
index e11d3075..79894c7d 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -8,7 +8,7 @@ pytest==4.6.6; python_version<"3.5"
 pytest==5.3.5; python_version>="3.5"
 six==1.14.0
 tornado==5.1.1; python_version<"3.6"
-tornado==6.0.3; python_version>="3.6"
+tornado==6.0.4; python_version>="3.6"
 trio==0.13.0; python_version>="3.6"
 outcome==1.0.1; python_version>="3.5"
 attrs==19.3.0; python_version>="3.5"