To rank Decision Making Units (DMU) in Data Envelopment Analysis (DEA), the peer-evaluation based cross-efficiency method is generally used. Indeed, in this method, each DMU is evaluated from the view point of other DMUs. In this article, a method is suggested which instead examines each DMU just by using the weights resulting from the evaluation of ideal and anti-ideal virtual DMUs and thus exhibits a new secondary goal that possibly prevents the existence of multiple weights in cross-efficiency evaluation, in addition to introducing a new cross-efficiency score. The advantage of this method over the others is that it needs less computations in determining the cross-efficiency score. To this end, some examples are illustrated which show how it differs with other methods.