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Many strategies have been introduced to add several types of constraints within the most well known algorithms for mining frequent patterns. The current one algorithm to find frequent items is FP-growth algorithm. Infrequent Itemset mining is a variation of frequent itemset mining where it finds the rare patterns ie, it finds the data items which occur very rarely. When there is need to minimize a certain cost function, discovering rare data correlations is more interesting than mining frequent ones. The existing method for discovery available in literature but there are some drawbacks related to itemset search space and large input database. The objective of this paper is to overcome these limitations. In this paper FP-Bonsai algorithm is proposed to find infrequent items. FP-Bonsai improve FP-growth performance by reducing (pruning) the FP-tree. In this algorithm, ExAnte data reduction technique is used in which double reduction is applied to find rare patterns. This technique is more efficient than existing methods in the context of reduction of search space ie reduction of memory requirement and reduction of large transactional database by applying constraints.