Symbolic cueing paradigm has been widely used to investigate the attention orienting induced by centrally-presented gaze or arrow cues. Previous studies have found a sequence effect in this paradigm when arrows are used as central cues and simple detection tasks are included. The present study investigated the universality of the sequence effect with gaze cues and in discrimination tasks. It was found that sequence effects are not limited to specific cue types or specific tasks, and the sequence effect can even generalize across different cue types (from gaze to arrow, or from arrow to gaze). In addition, the sequence effect is not influenced by the repetition and switch of target identities (along with response keys). The results suggest that sequential processing is a common mechanism in attention orienting systems, and support the automatic retrieval hypothesis more than the strategy adjustment account.