Various types of sequences in the human genome are known to play important roles in different aspects of genomic functioning. Among these sequences, palindromic nucleic acid sequences are one such type that have been studied in detail and found to influence a wide variety of genomic characteristics. For a nucleotide sequence to be considered as a palindrome, its complementary strand must read the same in the opposite direction. For example, both the strands i.e the strand going from 5' to 3' and its complementary strand from 3' to 5' must be complementary. A typical nucleotide palindromic sequence would be TATA (5' to 3') and its complimentary sequence from 3' to 5' would be ATAT. Thus, a new method has been developed using dynamic programming to fetch the palindromic nucleic acid sequences. The new method uses less memory and thereby it increases the overall speed and efficiency. The proposed method has been tested using the bacterial (3891 KB bases) and human chromosomal sequences (Chr-18: 74366 kb and Chr-Y: 25554 kb) and the computation time for finding the palindromic sequences is in milli seconds.