  We calculate the imaginary part of the induced pseudoscalar form factor of
the nucleon $G_P(t)$ in the framework of two-loop heavy baryon chiral
perturbation theory. The effect of the calculated three-pion continuum on the
pseudoscalar constant $g_P = (m_\mu/2M) G_P(t=-0.877m_\mu^2)$ measurable in
ordinary muon capture $\mu^-p\to \nu_\mu n$ turns out to be negligibly small.
Possible contributions from counterterms at two-loop order are numerically
smaller than the uncertainty of the dominant pion-pole term proportional to the
pion-nucleon coupling constant $g_{\pi N}= 13.2\pm 0.2$. We conclude that a
sufficiently accurate representation of the induced pseudoscalar form factor of
the nucleon at low momentum transfers $t$ is given by the sum of the pion-pole
term and the Adler-Dothan-Wolfenstein term: $G_P(t) = 4g_{\pi N} M f_\pi/
(m_\pi^2 -t)- 2g_A M^2 < r_A^2 >/3$, with $<r_A^2> = (0.44 \pm 0.02)$ fm$^2$
the axial mean square radius of the nucleon.
