In this study, we have tried to find the optimized design variables of the matching layer which is important part of thickness mode ultrasonic transducer and finally reach the conclusion that the electrical property of piezo-element must be under consideration when the optimized acoustic impedance is estimated. Proper expression of the effective impedance of front load at free resonant frequency(: $Z_{f}$ $^{(0)}$ /) has been induced by introducing the principle of binomial multilayer transformer and gradient based numerical method is utilized to find the most acceptable value of $Z_{ f}$/$^{(0)}$ . Optimized point of acoustic impedance can be calculated directly from $Z_{f}$ $^{(0)}$ using some simple formula which we propose. We also verify our result by both numerical and experimental method and get a good enhancement especially it concern to the bandwidth of ultrasonic transducer.