A new NDT method to detect ultrasonic flaw echoes close to the surface in strongly scattering materials is proposed. The method is based on high-resolution pursuit (HRP), which is a version of matching pursuit (MP) that emphasizes local fit over global fit. Since HRP produces representations which resolve closely spaced features, it is a very valuable signal processing tool for achieving the goal claimed in this work. Furthermore, HRP has the same order of complexity of MP. The good performance of the method is experimentally verified using ultrasonic traces acquired from a carbon fibre reinforced plastic (CFRP) material.