A variety V has directly decomposable congruences (abbreviated: DDCon) if every congruence relation on the product A x B of algebras A, B s V is uniquely determined by its projections onto A and B. Varieties with DDCon are characterizable by Mal'cev condition, the concrete polynomial identities were derived by G. A. Fraser and A. Horn [2] and by T.-K. Hu [unpublished]. These identities are not simple and so the phenomenon of DDCon was investigated on varieties with some additional assumptions, e.g. the Mal'cev characterization of DDCon in a permutable variety with one idempotent nullary operation is well-known, see H. Werner [9]. Recently, using H. Werner's description of permutable varieties [8], I. Chajda [1] gave a Mal'cev characterization of DDCon in permutable varieties only. We show (in Corollary 1 of this paper) that the identities of [1] can be improved; our improvement is slight in form but essential since the Mal'cev polynomial p(x = p(x, y, y) = p(y, y, x)) can be derived from the new identities and thus they characterize permutability and direct decomposability of congruences in an arbitrary variety of algebras, i.e. the assumption of permutability is redundant now (compare [1] and Corollary 1 of this paper). Making use of J. Hagemann's and A. Mitschke's description of n-permutable varieties, see [4], we generalize the above mentioned result and so a Mal'cev characterization for n-permutable varieties with DDCon is obtained. In order not to have to interrupt the discussion later, recall firstly some