Consider the linear dynamic system on time scales u(superscript Δ)=pv, v(superscript Δ)=-qu(superscript σ) (0.1) where p>0 and q are rd-continuous functions on a time scale T such that sup T=∞. When q(t) is allowed to take on negative values, we establish an oscillation criterion for system (0.1). Our result improves a main result of Fu and Lin [S. C. Fu and M. L. Lin, Oscillation and nonoscillation criteria for linear dynamic systems on time scales, Computers and Mathematics with Applications.