Rare itemset mining is a relatively recent topic of study in data mining. In certain application domains, such as online banking transaction analysis, sensor data analysis, and stock market analysis, rare patterns are patterns with low support and high confidence that are extremely interesting when compared to frequent patterns. Numerous applications generate large amounts of continuous data streams. We require efficient algorithms capable of processing data streams in order to analyze them and find unique patterns. The strategies developed for static databases cannot be used to data streams. As a result, we require algorithms created expressly for data stream processing in order to extract critical unique patterns. Rare pattern mining is still in its infancy, with only a few ways available. To address this is developed the Dynamic Support Range-based Hybrid-Eclat Algorithm (DSRHEA), an Eclat-based technique for mining unique patterns from a data stream using bit-set vertical mining with two item-based optimizations. The detected patterns are kept in a prefix-based rare pattern tree that uses double hashing to maintain the unusual pattern in the data stream. Testing showed that the proposed method did well in terms of how long it took to run ,how many rare patterns it made and accuracy.