The suboptimum detection procedure based on the weighting of partial decisions (WPD) was introduced as an improvement of one-bit-quantisation digital matched filtering, also known as binary matched filtering (BMF). The WPD is characterised by minimal additional hardware and software requirements but considerably better performance in comparison with BMF. A primary application of the WPD is the implementation of cost-effective medium-speed voice-band data medem receivers, but it can also be used in a number of other parametric and nonparametric detection problems. Formerly, the WPD was analysed only for binary transmission with an antipodal set of signalling waveforms. In this paper, the concept of the WPD is generalise and analysed theorectically forM-ary transmission with an arbitrary set of equal-energy signalling waveforms. Here, it is treated as the generalise procedure with BMF is its special case. The results of the performance analysis are provided, as well.