Similarity search in streaming time series is a crucial subroutine of a number of real-time applications dealing with time-series streams. In finding subsequences of time-series streams that match with patterns under Dynamic Time Warping (DTW), data normalization plays a very important role and should not be ignored. SPRING proposed by Sakurai et al. conducts the similarity search by mitigating the time and space complexity of DTW. Unfortunately, SPRING produces inaccurate results since no data normalization is taken into account before the DTW calculation. In this paper, we improve the SPRING method to deal with similarity search for prespecified patterns in streaming time series under DTW by applying incremental min-max normalization before the DTW calculation. For every pattern, our proposed method uses a monitoring window anchored at the entry of one streaming time series to keep track of min-max coefficients, and then the DTW distance between the normalized subsequence and the normalized pattern is incrementally computed. The experimental results reveal that our proposed method obtains best-so-far values better than those of another state-of-the-art method and the wall-clock time of the proposed method is acceptable.