Abstract: We considered the w-core EP inverse in involutive rings and discussed its properties from two aspects. On the one hand, the w-core EP decomposition was defined, and a new characterization of the w-core EP inverse was given through the w-core EP decomposition, and some new properties of the w-core EP invertible element were discussed. On the other hand, e=a^D_w(aw)^k+1, f=wa^D_w(aw)^ka and the projection element p=awa^D_w were introduced. The w-core EP core inverse was equivalently characterized
 by using e,f and the projection element p, and the w-core EP order a≤_wb was defined accordingly. The properties and its equivalent characterizations of the w-core EP order were studied.

Key words: w-core inverse, w-core EP inverse, w-core EP decomposition, w-core EP order