In this paper, we propose a new (t, n) threshold scheme. The scheme allows a user to divide portions of a secret among the designated group. Any t or more participants from a designated group of n members can cooperate to reconstruct the secret while (t-1) or less participants can not. Furthermore, the scheme provides an efficient mechanism to detect and identify cheaters. From the security analysis, we conclude that any participant does not have the ability to deceive other participants to obtain their portion of the secret. Therefore, this scheme is very practical for a broad spectrum of applications.