We introduce a new transform through a construction that we have called the Adaptive Vector Greedy Splitting algorithm. The main idea behind this algorithm is an optimization step based on the simple Bathtub Principle. We use the Vector Greedy Splitting algorithm to build orthonormal bases for a given vector of random variables (also called signals). A particular basis constructed in this way may be used for signal coompression, audio pattern recognition and other applications of signal processing. We compare performance of the Vector Greedy Splitting algorithm with the Haar wavelet transform applied to the same vector of input signals. The implementation of the algorithms and statistics accumulation are made using the ANSI C computer language and Matlab. The work uses advanced methods of Computer Engineering and Digital Signal Processing.