Smith-Waterman and Needleman-Wunsch are the most popular algorithms used for pairwise sequence alignment. The space and time complexity of these algorithms are quadratic. The biological sequences are composed of millions of base pairs. Hence, the quadratic space complexity becomes costlier in terms of storage requirement and performance. FastLSA algorithm addresses this problem by adapting to the amount of available memory. Minimum memory requirement for FastLSA is a linear function of sequence length, however if more memory is available, then it achieves better performance using the extra available memory. In this paper, we present Diagonal Linear Space Alignment algorithm which is an improvement over FastLSA. Our algorithm is adaptable to the amount of memory available, like FastLSA, but it stores the diagonals of the Dynamic Programming matrix unlike FastLSA which stores the rows and columns. We have analytically and experimentally proved that our algorithm performs better than FastLSA. Experimental results show that the proposed Diagonal Linear Space Alignment algorithm reduces the memory requirement by about 36% to 40% compared to FastLSA for similar performance in time. For longer sequences, our algorithm offers more performance gain over FastLSA.