In this paper, a novel intermittent compensation switching strategy is designed for the stabilization of switched nonlinear systems. By making use of composite multiple Lyapunov-like functions, the designed switching strategy intermittently checks the worst direction of state and then compensates for the corresponding worst state. The associated Lyapunov-like functions are allowed to increase their values both during the active interval and at the switching instant. This removes the two conservative nonincreasing requirements which are commonly used in the classical switching law design. Practically, to implement the switching strategy, we only need to check the switching conditions and transmit the state information on a discrete time sequence, and Zeno behavior is avoided with a dwell-time in the nonlinear situation. Some sufficient conditions in their algebraic forms are proposed to make the equilibrium point of the closed-loop systems asymptotically stable. An example demonstrates the effectiveness.