  We develop a methodology for estimating parity-odd bispectra in the cosmic
microwave background (CMB). This is achieved through the extension of the
original separable modal methodology to parity-odd bispectrum domains ($\ell_1
+ \ell_2 + \ell_3 = {\rm odd}$). Through numerical tests of the parity-odd
modal decomposition with some theoretical bispectrum templates, we verify that
the parity-odd modal methodology can successfully reproduce the CMB bispectrum,
without numerical instabilities. We also present simulated non-Gaussian maps
produced by modal-decomposed parity-odd bispectra, and show the consistency
with the exact results. Our new methodology is applicable to all types of
parity-odd temperature and polarization bispectra.
