diff --git a/index.bs b/index.bs
index a3600b25..14da50cc 100644
--- a/index.bs
+++ b/index.bs
@@ -12794,8 +12794,6 @@ The \[[Prototype]] [=/internal slot=] of an [=asynchronous iterator prototype ob
             |interface|, given |object|'s [=default asynchronous iterator object/target=], |object|,
             and |value|.
 
-    1.  Let |returnStepsPromise| be null.
-
     1.  Let |ongoingPromise| be |object|'s [=default asynchronous iterator object/ongoing promise=].
 
     1.  If |ongoingPromise| is not null, then:
@@ -12803,18 +12801,20 @@ The \[[Prototype]] [=/internal slot=] of an [=asynchronous iterator prototype ob
         1.  Let |onSettled| be [$CreateBuiltinFunction$](|returnSteps|, « »).
         1.  Perform [$PerformPromiseThen$](|ongoingPromise|, |onSettled|, |onSettled|,
             |afterOngoingPromiseCapability|).
-        1.  Set |returnStepsPromise| to |afterOngoingPromiseCapability|.\[[Promise]].
+        1.  Set |object|'s [=default asynchronous iterator object/ongoing promise=] to
+            |afterOngoingPromiseCapability|.\[[Promise]].
 
     1.  Otherwise:
-        1.  Set |returnStepsPromise| to the result of running |returnSteps|.
+        1.  Set |object|'s [=default asynchronous iterator object/ongoing promise=] to the result of
+            running |returnSteps|.
 
     1.  Let |fulfillSteps| be the following steps:
         1.  Return [$CreateIterResultObject$](|value|, <emu-val>true</emu-val>).
 
     1.  Let |onFulfilled| be [$CreateBuiltinFunction$](|fulfillSteps|, « »).
 
-    1.  Perform [$PerformPromiseThen$](|returnStepsPromise|, |onFulfilled|,
-        <emu-val>undefined</emu-val>, |returnPromiseCapability|).
+    1.  Perform [$PerformPromiseThen$](|object|'s [=default asynchronous iterator object/ongoing
+        promise=], |onFulfilled|, <emu-val>undefined</emu-val>, |returnPromiseCapability|).
 
     1.  Return |returnPromiseCapability|.\[[Promise]].
 </div>