This paper proposes an effective data mining technique for finding useful patterns in streaming sequences. At present, typical approaches to this problem are to search for patterns in a fixed-size window sliding through the stream of data being collected. The practical values of such approaches are limited in that, in typical application scenarios, the patterns are emerging and it is difficult, if not impossible, to determine a priori a suitable window size within which useful patterns may exist. It is therefore desirable to devise techniques that can identify useful patterns with arbitrary window sizes. Attempts to this problem are challenging, however, because it requires a highly efficient searching in a substantially bigger solution space. This paper presents a new method which includes firstly a pruning strategy to reduce the search space and secondly a mining strategy that adopts a dynamic index structure to allow efficient discovery of emerging patterns in a streaming sequence. Experimental results on real data and synthetic data show that the proposed method outperforms other existing schemes both in computational efficiency and effectiveness in finding useful patterns.