  We study the possible quantum anomaly for the transverse Ward-Takahashi
relations in four dimensional gauge theories based on the method of computing
the axial-vector and the vector current operator equations. In addition to the
well-known anomalous axial-vector divergence equation (the Adler-Bell-Jackiw
anomaly), we find the anomalous axial-vector curl equation, which leads to the
quantum anomaly of the transverse Ward-Takahashi relation for the axial-vector
vertex. The computation shows that there is no anomaly for the transverse
Ward-Takahashi relation for the vector vertex.
