Authentication of individuals is rapidly becoming an important issue. On-line signature verification is one of the methods that use biometric features. This paper proposes a new HMM algorithm is for on-line signature verification. After preprocessing, input signature is discretized in a polar coordinate system. This particular discretization leads to a simple procedure for assigning initial state and state transition probabilities.This paper utilizes only pen position trajectories, no other information is used which makes the algorithm simple and fast. A preliminary experiment shows that the proposed algorithm appears to be promising.