The method developed in [A.J. Durán, F.A. Grünbaum, Orthogonal matrix polynomials satisfying second order differential equations, Int. Math. Res. Not. 10 (2004) 461–484] led us to consider matrix polynomials that are orthogonal with respect to weight matrices W ( t ) of the form e − t 2 T ( t ) T ∗ ( t ) , t α e − t T ( t ) T ∗ ( t ) , and ( 1 − t ) α ( 1 + t ) β T ( t ) T ∗ ( t ) , with T satisfying T ′ = ( 2 B t + A ) T , T ( 0 ) = I , T ′ = ( A + B / t ) T , T ( 1 ) = I , and T ′ ( t ) = ( − A / ( 1 − t ) + B / ( 1 + t ) ) T , T ( 0 ) = I , respectively. Here A and B are in general two non-commuting matrices. We are interested in sequences of orthogonal polynomials ( P n ) n which also satisfy a second order differential equation with differential coefficients that are matrix polynomials F 2 , F 1 and F 0 (independent of n ) of degrees not bigger than 2, 1 and 0 respectively. To proceed further and find situations where these second order differential equations hold, we only dealt with the case when one of the matrices A or B vanishes. The purpose of this paper is to show a method which allows us to deal with the case when A , B and F 0 are simultaneously triangularizable (but without making any commutativity assumption).