The authors consider the linear matrix Hamiltonian system \[ X'=A(t)X+B(t)Y,\quad Y'=C(t)X-A^*(t)Y,\quad t\geq t_0, \] where \(X(t), Y(t), A(t), B(t)=B^*(t)>0\) and \(C(t)=C^*(t)\) are \(n\times n\)-matrices whose entries real-valued continuous functions. By employing the substitution \(W(t)=a(t)[Y(t)X^{-1}(t)+f(t)B^{-1}(t)]\) and a fundamental matrix \(\Phi(t)\) for the linear equation \(v'=A(t)v\), they show that \(R(t)=\Phi^*(t)W(t)\Phi(t)\) solves a matrix Riccati equation. Based on this Riccati equation and the \(H\)-function averaging method, they establish some new interval oscillation criteria for the system above. Among earlier published papers on the subject are \textit{Q. Kong} [Differ. Equ. Dyn. Systems, 8, 99-110 (2000; Zbl 0993.34034)]; \textit{Q. G. Yang} [Ann. Pol. Math., 79, 185-198 (2002; Zbl 1118.34315)] and \textit{Q.-R. Wang} [J. Math. Anal. Appl., 276 373--395 (2002; Zbl 1022.34032)].