Time series data stream mining has attracted considerable research interest in recent years. Pattern discovery is a challenging problem in time series data stream mining. Because the data update continuously and the sampling rates may be different, dynamic time warping (DTW)-based approaches are used to solve the pattern discovery problem in time series data streams. However, the naive form of the DTW-based approach is computationally expensive. Therefore, Toyoda proposed the CrossMatch (CM) approach to discover the patterns between two time series data streams (sequences), which requires only O(n) time per data update, where n is the length of one sequence. CM, however, does not support normalization, which is required for some kinds of sequences (e.g. stock prices, ECG data). Therefore, we propose a normalized-CrossMatch approach that extends CM to enforce normalization while maintaining the same performance capabilities.