The authors study the linear matrix system
where , , are continuous real-valued -matrix functions on the interval and is a real-valued continuous function on . The matrices and are supposed to be symmetric and is supposed to be either positive definite or negative definite. The authors transform the system by a transformation preserving oscillatory properties into a Hamiltonian system and use an oscillation criterion due to I. Kumari and S. Umamaheswaram [J. Differ. Equations 165, No.1, 174-198 (2000; Zbl 0970.34025)] to derive a new oscillation criterion for system (1).