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Let A 1 , A 2 ,....An be the given sequence of n matrices, generally matrix chain multiplication algorithm is used to obtain its-product with minimum cost(lowest cost). However the matrix chain multiplication is a dynamic programming paradigm and takes O(n 3 ) computational complexity. Here we present improved algorithm for matrix chain multiplication with minimum space and time complexities. The viability of this new algorithm is demonstrated using few examples and the performance is computationally verified. This algorithm does not take O(n 3 ) if any two of the S values are not same and O(n 3 ) when the two values of S are same in the worst case.

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