  The recent TRIUMF experiment for $\mu^- p \to n \nu_{\mu} \gamma$ gave a
surprising result that the induced pseudoscalar coupling constant $g_P$ was
larger than the value obtained from $\mu^- p \to n \nu_{\mu}$ experiment as
much as 44 %. Reexamining axial vector current on the gauge theory, we found an
additional term to the matrix element of Beder and Fearing which was used to
extract the $g_P$ value from the measured photon energy spectrum. This
additional term, which is self gauge invariant, plays a key role in restoring
the reliability of $g_P (- 0.88 m_{\mu}^2) = 6.77 g_A (0)$. Comparison with
conventional approaches is also presented.
