String Matching is now a prominent field in the area of Computer Science and it has many applications in the real world. A new algorithm for Suffix Search which uses chained hashing is proposed and this works well in matched case and mismatched case. A separate hash function is introduced in this paper. Hash functions can be declared in many ways. In this, radix hashing is used and the need of the shift table used in these algorithms can be avoided. Every pattern matching algorithm consists of mainly two phases. They are the preprocessing phase and the matching phase. Each of these phases has its own time complexity as well as space complexity. The proposed method has very low time complexity in average case.