The auroral electrojet index is an important index in monitoring and predicting substorms. A substorms usually includes auroral breakup, auroral electrojet event marked by AE increase, energetic particle injection at geosynchronous orbit, mid-low latitude Pi2, etc. However the question whether an auroral electrojet event corresponds to a substorm remains unanswered. Using the auroral electrojet index in 2004, we analyzed five auroral electrojet events and studied their relation with substorms. The results show that there are three kinds of auroral electrojet events: (1) simultaneous rapid increase of westward auroral electrojet and eastward auroral electrojet; (2) rapid increase of westward auroral electrojet and almost unchangeable eastward auroral electrojet; (3) rapid increase of eastward auroral electrojet and almost unchangeable westward auroral electrojet. Most of auroral electrojet events correspond to substorms. However a few auroral electrojet events are not accompanied by substorms. This situation most often occurs for the auroral electrojet event in which eastward auroral electrojet dominates.