  We propose an extended formalism for the spectral broadening function (BF)
based on the multiplication rule of block matrices. The formalism, which we
named the binary broadening function (BBF), can produce decomposed BFs for
individual components of a binary star system by using two spectral templates.
The decomposed BFs can be used to derive precise rotational profiles and radial
velocities for individual components. We test the BBF on simulated spectra and
actual observational spectra to show that the method is feasible on
spectroscopic binaries, even when the spectral lines of two stellar components
are heavily blended. To demonstrate the capability of the method, we conduct a
simulation of `sketching' (imaging) a transiting circumbinary exoplanet using
the BBF. We also discuss issues of implementation such as the variation of BBF
with biased templates, the pros and cons of BBF, and cases when the method is
not applicable.
