A natural number based linear time filtering approach to finding all occurrences of a DNA pattern

String matching and searching techniques have been extensively studied in different research works. They currently play an essential part in the field of computational biology. Most of those techniques, from classics to their improved versions could successfully accomplish the task in linear time. In this paper, I propose a new searching approach based on the delivery of distinct natural numbers over a transition matrix of four nucleotides to find all occurrences of a DNA pattern in a given string. My algorithm has only Theta(n - 1) time complexity for the worst case with n to be the length of a given string s for a DNA pattern p of length m to be searched on.