In this paper, we present a new TU complex detection and characterization algorithm that consists of two stages; the first is a mathematical modeling of the electrocardiographic segment after QRS complex; the second uses classic threshold comparison techniques, over the signal and its first and second derivatives, to determine the significant points of each wave. Later, both T and U waves are morphologically classified. Amongst the principal innovations of this algorithm is the inclusion of U-wave characterization and a mathematical modeling stage, that avoids many of the problems of classic techniques when there is a low signal-to-noise ratio or when wave morphology is atypical. The results of the algorithm validation with the recently appeared QT database are also shown. For T waves these results are better when compared to other existing algorithms. U-wave results cannot be contrasted with other algorithms as, to our knowledge, none are available. Examples showing the causes of principal discrepancies between our algorithm and the QT database annotations are also given, and some ways of attempting to improve and benefit from the proposed algorithm are suggested.