It is known that, in the scalar case, a good via to compute recurrence coefficients of polynomials orthogonal with respect to a nonnegative measure is the modified Chebyshev algorithm [cf. \textit{R. A. Sack} and \textit{A. F. Donavan}, Numer. Math. 18, 465-478 (1972; Zbl 0221.65041)]. This algorithm, recently extended to the vector case [cf. \textit{Zelia da Rocha}, Numer. Algorithms 20, No. 2-3, 139-164 (1999; Zbl 0941.42011)], employs the so-called modified moments instead of the ordinary ones. On applying such an algorithm, it has been also shown that there exists an important difficulty to choose the reference polynomials required for the underlying modified moments [cf. \textit{B. Beckermann} and \textit{E. Bourreau}, J. Comput. Appl. Math. 98, No. 1, 81-98 (1998; Zbl 0935.65011)]. In this paper the author, by using the concept of matrix biorthogonality, presents a vector version of the above modified algorithm. Several numerial examples are discussed and possible suitable choices for the reference polynomial pointed out.