Maximum entropy principle in nonextensive statistical mechanics is formulated in two different ways in the literature. One uses the basic original probability distribution p i and the other is described solely by the escort distribution associated with p i. Though at first glance these two formulations are equivalent, actually they are different each other. The entropy functional written in terms of the escort distribution is not always concave for the entropic index q>0, in marked contrast to the original Tsallis entropy. It is emphasized that the escort distribution is a secondary object calculated from the basic original distribution.