We investigate the problem of verifying the absence of zeno executions in a hybrid system. A zeno execution is one in which there are infinitely many mode switches in a finite time interval. The presence of zeno executions poses challenges towards implementation and analysis of hybrid control systems. We present a simple transformation of the hybrid system which reduces the non-zenoness verification problem to that of termination, that is, the original system has no zeno executions if and only if the transformed system has no non-terminating executions. This provides both theoretical insights and practical techniques for non-zenoness verification. We illustrate the feasibility of our approach by applying it on hybrid system examples.