An ultrasonic self-calibrating technique for the characterization of a ceramic which was fabricated by change pressing time during the HIP process has been applied by using the ratio of the reflection and transmission coefficients of normal incidence longitudinal waves. The ratio is self-compensated, in that it is independent of the characteristics for transmission and reception of ultrasound by the transducer and the condition of the couplant. The insensitive direction in parameter space is defined as the direction in which the variation of the ratio to changes of two parameters vanishes. For inverse problem the distribution of minima in an error surface is investigated.