Second language (L2) speech is often labelled with the native, phoneme categories. Hence, we often observe segments for which it is difficult, if not impossible, to decide on a categorical phoneme label. We refer to these segments as “non-categorical” phoneme units. Existing approaches to mispronunciation detection and diagnosis (MDD) mostly focus on categorical phoneme errors, where one native phoneme is substituted for another. However, noncategorical errors are not considered. To better represent L2 speech for improved MDD, this work aims to discover an Extended Phoneme Set in L2 speech (L2-EPS) which includes not only the categorical phonemes based on the native set, but also non-categorical phoneme units. We apply an optimized k-means algorithm to cluster phoneme-based phonemic posterior-grams (PPGs), which are generated through an acoustic-phonemic model (APM). Then we find the L2-EPS based on analysis of the clusters obtained. We verified experimentally that the non-categorical phonemes in L2-EPS can extend the native phoneme categories to better describe L2 speech. Hence L2-EPS can enrich the existing approaches to MDD for better performance.