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We consider the N=1 supersymmetric QCD with SU(N_c) gauge group involving  N_f = N_c - 1 pairs of chiral matter multiplets in fundamental andantifundamental color representations. For this theory in the framework of theeffective lagrangian approach, we solve the BPS equations for the domain wallsinterpolating between different vacua. The equations always have a uniquesolution for the walls interpolating between the chirally symmetric and achirally asymmetric vacua. For the walls interpolating between differentchirally asymmetric vacua, the equations admit two different solutions whichexist when the mass of the matter field is below some critical value m*. At m =m*, two branches join together and, at m > m*, no BPS - saturated complexdomain walls exist.Comment: 25 pages, LaTeX including 7 Postscript figures; typos correcte

BPS domain walls in supersymmetric QCD: Higher unitary groups