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The axial transmission technique uses a linear arrangement of ultrasonic emitters and receivers placed on a same side of a cortical bone site in contact with the skin, involving ultrasonic propagation along the axis of bone. The velocity of the waves radiated from bone has been shown to reflect bone status. The thickness and composition of soft tissue may vary along the length of the bone, between different skeletal sites, or between subjects. Hence, accurate estimates of velocity require first to eliminate the effect of the overlying soft tissue that is traversed by the ultrasound wave. To correct for such bias without measuring soft tissue properties, we designed new ultrasonic probes in the 1-2 MHz frequency range. It is based on propagation along the bone surface in two opposite directions from two sources placed on both sides of a unique group of receivers. The aim is to obtain an unbiased estimate of the velocity without any intermediate calculation of soft tissue properties, such as thickness variation or velocity. Validation tests were performed on academic material such as Perspex or aluminium. We found that head wave velocity values could be biased by more than 10% for inclination of a few degrees between the test specimen surface and the probe. On test materials, the compensation procedure implemented in our probe led to a relative precision error on velocity measurement lower than 0.2 to 0.3%. These results suggest that the correction procedure allows measuring in vivo velocities independently of soft tissue properties.