This paper concerns with the master-slave exponential synchronization analysis for a class of general Lur'esystems with time delay.Different from the previous methods based on the differential inequality technique, a newapproach is proposed to derive some new exponential synchronization criteria.The restriction that the control widthhas to be larger than the time delay is removed.This leads to a larger application scope for our method.Moreover, notranscendental equation is involved in the obtained result, which reduces the computational burden.Two examples aregiven to validate the theoretical results.