The evolution of a Stokes vector through depolarizing media is considered. A general form for the differential matrix is derived that is appropriate in the presence of depolarization, and is parameterized in a manner that ensures that it yields, upon integration, a valid Mueller matrix for any choice of parameters with some limited constraints. The form expands the more limited form for a non-depolarizing matrix given by Azzam [J. Opt. Soc. Am. 68, 1756-1767 (1978)] and which was extended recently by others to include depolarization. A decomposition for a Mueller matrix is proposed, based upon the parameters for the differential matrix, which when integrated over unit length, would yield the same Mueller matrix.