We give the relation between Hermite–Pade approximants and vector orthogonal polynomials. An algorithm for calculating vector orthogonal polynomials near the diagonal is described. An exact multiple integral formula for vector orthogonal polynomials is proved. An example is given showing how the recurrence relations of Pade may be used to calculate Hermite–Pade approximants of degrees $m,\mu ,\mu $, with $\mu $ increasing.