The threshold value of the traitor-tracing schemes means a maximum number of traitors whose identities can be uniquely exposed using the tracing scheme. In the traitor-tracing scheme based on an error-correcting code, which is focused at this paper, the threshold value is determined by the error-correcting capability of the underlying error-correcting code. Analyzed in terms of a combinatorial property of the tracing scheme is the resulting effect on the tracing scheme when the collusion size is over the threshold value, and a possibility of two disjoint groups of users making an identical unauthorized decryption key is shown.