By using the generalized Riccati technique and the averaging technique, we establish new oscillation criteria for the second order self-adjoint matrix differential system with damping
(P(t)Y'(t))' + r(t)P(t)Y'(t) + Q(t)Y(t) = 0, t ≥ t₀.
The criteria are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t₀,∞), rather than on the whole half-line. In particular, our results complement a number of existing results and handle a case that is not covered by known criteria. Moreover, examples indicating the importance of our results are also included.