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Matrix multiplication is a very common operation performed in many real world applications. So much of research has been done in reducing the time complexity of multiplying two matrices by researchers like Strassen, Don Coppersmith, Shmuel Winograd etc. All mathematical software also rely upon the common matrix multiplication algorithm. But, if the matrices that has to be applied has some special properties in some applications, then their multiplication complexity can be reduced. So, in this paper a new algorithm for multiplying a special kind of n x n matrices which are used in analyzing electrical circuits is devised. This algorithm outperforms the previous fast recursive algorithm for matrix multiplication.