diff --git a/crates/bevy_transform/src/systems.rs b/crates/bevy_transform/src/systems.rs
index e7bd9789d3df7..672e67b513523 100644
--- a/crates/bevy_transform/src/systems.rs
+++ b/crates/bevy_transform/src/systems.rs
@@ -113,7 +113,7 @@ mod test {
 
         let mut update_stage = SystemStage::parallel();
         update_stage.add_system(parent_update_system);
-        update_stage.add_system(transform_propagate_system);
+        update_stage.add_system(transform_propagate_system.after(parent_update_system));
 
         let mut schedule = Schedule::default();
         schedule.add_stage("update", update_stage);
@@ -158,7 +158,7 @@ mod test {
 
         let mut update_stage = SystemStage::parallel();
         update_stage.add_system(parent_update_system);
-        update_stage.add_system(transform_propagate_system);
+        update_stage.add_system(transform_propagate_system.after(parent_update_system));
 
         let mut schedule = Schedule::default();
         schedule.add_stage("update", update_stage);
@@ -201,7 +201,7 @@ mod test {
 
         let mut update_stage = SystemStage::parallel();
         update_stage.add_system(parent_update_system);
-        update_stage.add_system(transform_propagate_system);
+        update_stage.add_system(transform_propagate_system.after(parent_update_system));
 
         let mut schedule = Schedule::default();
         schedule.add_stage("update", update_stage);
@@ -286,7 +286,7 @@ mod test {
         let mut app = App::new();
 
         app.add_system(parent_update_system);
-        app.add_system(transform_propagate_system);
+        app.add_system(transform_propagate_system.after(parent_update_system));
 
         let translation = vec3(1.0, 0.0, 0.0);
 
@@ -339,19 +339,20 @@ mod test {
     #[test]
     #[should_panic]
     fn panic_when_hierarchy_cycle() {
-        let mut app = App::new();
+        let mut world = World::default();
+        // This test is run on a single thread in order to avoid breaking the global task pool by panicking
+        // This fixes the flaky tests reported in https://github.com/bevyengine/bevy/issues/4996
+        let mut update_stage = SystemStage::single_threaded();
 
-        app.add_system(parent_update_system);
-        app.add_system(transform_propagate_system);
+        update_stage.add_system(parent_update_system);
+        update_stage.add_system(transform_propagate_system.after(parent_update_system));
 
-        let child = app
-            .world
+        let child = world
             .spawn()
             .insert_bundle((Transform::identity(), GlobalTransform::default()))
             .id();
 
-        let grandchild = app
-            .world
+        let grandchild = world
             .spawn()
             .insert_bundle((
                 Transform::identity(),
@@ -359,13 +360,13 @@ mod test {
                 Parent(child),
             ))
             .id();
-        app.world.spawn().insert_bundle((
+        world.spawn().insert_bundle((
             Transform::default(),
             GlobalTransform::default(),
             Children::with(&[child]),
         ));
-        app.world.entity_mut(child).insert(Parent(grandchild));
+        world.entity_mut(child).insert(Parent(grandchild));
 
-        app.update();
+        update_stage.run(&mut world);
     }
 }