diff --git a/scheduler.go b/scheduler.go
index 0026185..9dbfa1b 100644
--- a/scheduler.go
+++ b/scheduler.go
@@ -44,9 +44,6 @@ type Scheduler struct {
 	// to avoid using cron.EntryID as the public API of
 	// the Scheduler.
 	idmap map[string]cron.EntryID
-	// When a Scheduler has been created with an existing Redis connection, we do
-	// not want to close it.
-	sharedConnection bool
 }
 
 const defaultHeartbeatInterval = 10 * time.Second
@@ -54,12 +51,18 @@ const defaultHeartbeatInterval = 10 * time.Second
 // NewScheduler returns a new Scheduler instance given the redis connection option.
 // The parameter opts is optional, defaults will be used if opts is set to nil
 func NewScheduler(r RedisConnOpt, opts *SchedulerOpts) *Scheduler {
+	scheduler := newScheduler(opts)
+
 	redisClient, ok := r.MakeRedisClient().(redis.UniversalClient)
 	if !ok {
 		panic(fmt.Sprintf("asynq: unsupported RedisConnOpt type %T", r))
 	}
-	scheduler := NewSchedulerFromRedisClient(redisClient, opts)
-	scheduler.sharedConnection = false
+
+	rdb := rdb.NewRDB(redisClient)
+
+	scheduler.rdb = rdb
+	scheduler.client = &Client{broker: rdb, sharedConnection: false}
+
 	return scheduler
 }
 
@@ -67,6 +70,15 @@ func NewScheduler(r RedisConnOpt, opts *SchedulerOpts) *Scheduler {
 // The parameter opts is optional, defaults will be used if opts is set to nil.
 // Warning: The underlying redis connection pool will not be closed by Asynq, you are responsible for closing it.
 func NewSchedulerFromRedisClient(c redis.UniversalClient, opts *SchedulerOpts) *Scheduler {
+	scheduler := newScheduler(opts)
+
+	scheduler.rdb = rdb.NewRDB(c)
+	scheduler.client = NewClientFromRedisClient(c)
+
+	return scheduler
+}
+
+func newScheduler(opts *SchedulerOpts) *Scheduler {
 	if opts == nil {
 		opts = &SchedulerOpts{}
 	}
@@ -93,8 +105,6 @@ func NewSchedulerFromRedisClient(c redis.UniversalClient, opts *SchedulerOpts) *
 		state:             &serverState{value: srvStateNew},
 		heartbeatInterval: heartbeatInterval,
 		logger:            logger,
-		client:            NewClientFromRedisClient(c),
-		rdb:               rdb.NewRDB(c),
 		cron:              cron.New(cron.WithLocation(loc)),
 		location:          loc,
 		done:              make(chan struct{}),
@@ -294,9 +304,6 @@ func (s *Scheduler) Shutdown() {
 	if err := s.client.Close(); err != nil {
 		s.logger.Errorf("Failed to close redis client connection: %v", err)
 	}
-	if !s.sharedConnection {
-		s.rdb.Close()
-	}
 	s.logger.Info("Scheduler stopped")
 }