The design of Model-Reference Adaptive Control for MIMO linear systems has not yet achieved, in spite of significant efforts, the completeness and simplicity of its SISO counterpart. One of the main obstacles has been the generalization of the SISO assumption that the sign of the high-frequency gain (HFG) is known. Here we overcome this obstacle and present a more complete MIMO analog to the well known Lyapunov-based SISO design which is significantly less restrictive than the existing analogs. Our algorithm makes use of a new control parametrization derived from a factorization of the HFG matrix K-p = SDU, where S is symmetric positive definite, D is diagonal, and U is unity upper triangular. Only the signs of the entries of D or, equivalently, the signs of the leading principal minors of K-p, are assumed to be known. (C) 2003 Elsevier Science Ltd. All rights reserved.