The authors consider the linear matrix Hamiltonian system
where and are -matrices whose entries real-valued continuous functions. By employing the substitution and a fundamental matrix for the linear equation , they show that solves a matrix Riccati equation. Based on this Riccati equation and the -function averaging method, they establish some new interval oscillation criteria for the system above. Among earlier published papers on the subject are Q. Kong [Differ. Equ. Dyn. Systems, 8, 99-110 (2000; Zbl 0993.34034)]; Q. G. Yang [Ann. Pol. Math., 79, 185-198 (2002; Zbl 1118.34315)] and Q.-R. Wang [J. Math. Anal. Appl., 276 373–395 (2002; Zbl 1022.34032)].