In this paper we propose a matrix minimization algorithm for linear, time-invariant, implicit (E,A,B,C) descriptions of the type : E(x)over dot-(t) = As(t) + Bu(t); y(t) = Cx(t). Given the initial matrices (E,A,B,C), we obtain an externally equivalent minimal realization (E-m, A(m), B-m, C-m,) after applying a matricial procedure based on maximal, row and column, compressions.