Analytic hierarchy process (AHP) has been considerably criticized for possible rank reversal phenomenon caused by the addition or deletion of an alternative. This paper looks into the cause of rank reversal phenomenon and finds that rank reversal is caused by change of local priorities before and after an alternative is added or deleted. An approach is therefore proposed to keep the local priorities unchanged to avoid rank reversal phenomenon. Two well-known numerical examples are re-examined using the proposed approach to demonstrate its validity and practicability in rank preservation.