Öz n this paper we define an absolute summability by a series-to-sequence transfor­ mation matrix. We obtain tbe necessary and sufficient conditions in order that every absolutely convergent series is absolutely summable by series-to-sequence transfor­ mation matrix. For this we find new classes of matrices-conservative series-to-sequence transformation matrices and regular series-to-sequence transformation matrices. We study the relation of these two new classes of matrices with K, p,T and y-matrices. Finally we prove that the absolute summability of an absolutely convergent series by a matrix and the generalized limit of its absolute partial sum are equal under the suitable relation between the two matrices.