Ultrasonic measurements using orthogonal collimated beams provide both complementary and redundant information about internal parts of pieces or structures being tested, which must be fused. In this paper, a new wavelet-based digital processing technique which fuses ultrasonic pulse-echo traces obtained from several transducers located in two perpendicularly-coupled arrays is proposed. This is applied to accurately visualize the location of a small internal reflector by means of two dimensional (2D) displays. A-scans are processed in wavelet domain and fused in a common 2D pattern. A mathematical expression of the resulting 2D signal-to-noise ratio (SNR) is derived, and its accuracy is confirmed using benchmark tests performed with simulated registers and real measurements acquired using a multi-channel laboratory prototype. The measurement system consists of two properly-coupled perpendicular arrays comprising 4 square pulsed transducers and electronic driving circuitry. This technique improves 2D-SNR by a factor of twice the number of bands. In addition, good reflector location is obtained, since sub-millimeter 2D resolutions are achieved, despite only requiring eight ultrasonic channels. This good performance is confirmed by comparing the new wavelet fusing method with the two previously described techniques.