In the nonlinear ultrasonic technique, the measurement of the absolute acoustic nonlinearity parameter is employed to obtain quantitative material nonlinearity. In the piezoelectric method, this measurement involves two processes: calibration and harmonic measurements. In the calibration process, a transfer function is obtained, and distortion of the propagating wave is measured in the harmonic measurement. In the conventional method for this measurement, a narrowband pulser is typically used for the harmonic measurement, while a broadband pulser is used for the calibration measurement. In this study, we propose a technique that utilizes a narrowband pulser for both harmonic and calibration measurements. First, we introduced the proposed method to measure the transfer function in the calibration measurement employing the narrowband pulser. Then, we compared the results of the transfer functions and the absolute acoustic nonlinearity parameters obtained using both a narrowband and broadband pulser in the calibration. Based on the experimental results, we found that the results obtained using both the proposed and conventional methods are highly similar, confirming the validity of the proposed measurement technique. In conclusion, even though we exclusively employ the narrowband pulser, we can accurately measure the absolute nonlinearity parameter, leading to a reduction in the required measurement equipment.