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By using a monotonic functional on a suitable matrix space, some new oscillation criteria for self-adjoint matrix Hamiltonian systems are obtained. They are different from most known results in the sense that the results of this paper are based on information only for a sequence of subintervals of [t0, ∞), rather than for the whole half-line. We develop new criteria for oscillations involving monotonic functionals instead of positive linear functionals or the largest eigenvalue. The results are new, even for the particular case of self-adjoint second-differential systems which can be applied to extreme cases such as