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The purpose of the present paper is to introduce and study a Finsler space, called special C v-reducible, for which the Cartan v-covariant derivative of the Cartan tensor C ijk is written in a special form. A necessary and sufficient condition for a special semi-C-reducible Finsler space to be special C v-reducible is determined. Finally, a three dimensional special C v-reducible Finsler space illustrates the developed theory. M.S.C. 2010: 53B40, 53C60.fatcat:7d26im4qhvaijf6g4tomds2tqq