A good task allocation algorithm should find available processors for incoming jobs, if they exist, with minimum overhead. Due to its topological generality and flexibility the k-ary n-cube architecture has been chosen for the task allocation problem. We propose a fast and efficient isomorphic processor allocation scheme for kary n-cube systems by using isomorphic partitioning where the processor space is partitioned into higher dimensional isomorphic subcube and by using Subcube recognition ability algorithm (SRA) which uses simple coordinate calculation and spatial subtraction. Thus the proposed scheme seeks to reduce the search space drastically, and hence can locate a free subcube very quickly providing scalable, faster, processor allocation, complete recognition ability with minimal overhead and minimizes the fragmentation