We propose a new search algorithm for maximal 1-complete regions in high dimensional dense binary datasets. A maximal 1-complete region indicates a poten- tial functional cluster, and it is mathematically equivalent to a formal concept and also a closed itemset. Our algo- rithm is designed for dense datasets, where the percentage of 1?s in the dataset is higher than 10%, and the total num- ber of maximal 1-complete regions is much larger than the number of objects in the dataset. Our algorithm is memory efficient and unlike other closed set mining algorithms, it does not require all patterns mined so far to be kept in the memory. We show that our algorithm has solid theoretical foundations, and it is also very time efficient compared with other existing algorithms.