  The metric perturbation induced by a particle in the Schwarzschild background
is usually calculated in the Regge-Wheeler (RW) gauge, whereas the
gravitational self-force is known to be given by the tail part of the metric
perturbation in the harmonic gauge. Thus, to identify the gravitational
self-force correctly in a specified gauge, it is necessary to find out a gauge
transformation that connects these two gauges. This is called the gauge
problem. As a direct approach to solve the gauge problem, we formulate a method
to calculate the metric perturbation in the harmonic gauge on the Schwarzshild
backgound. We apply the Fourier-harmonic expansion to the metric perturbation
and reduce the problem to the gauge transformation of the Fourier-harmonic
coefficients (radial functions) from the RW gauge to the harmonic gauge. We
derive a set of decoupled radial equations for the gauge transformation. These
equations are found to have a simple second-order form for the odd parity part
and the forms of spin $s=0$ and 1 Teukolsky equations for the even parity part.
As a by-product, we correct typos in Zerilli's paper and present a set of
corrected equations in Appendix.
