This study summarizes the concept of cross efficiency derived from data envelopment analysis (DEA) and analyzes the cross efficiency related issues. The cross efficiency is a generalization of the traditional CCR model and widely applied to many fields. It is based on peer-evaluation, linking the performance of one decision-making unit (DMU) with others. Many scholars have studied cross efficiency from different aspects, but the non-uniqueness of the DEA optimal weights may still suppress the effectiveness of cross-efficiency evaluations. To address this uniqueness problem, this paper generalizes the original DEA cross-efficiency concept to a mutually acceptable cross-evaluation efficiency. Two numerical examples illustrate the power and suitability of the proposed algorithm to improve the cross-efficiency scores of the DMUs.