  The definition of the Galactic coordinate system was announced by the IAU
Sub-Commission 33b on behalf of the IAU in 1958. For more than 50 years the
definition of the Galactic coordinate system has remained unchanged from this
IAU1958 version. On the basis of deep and all-sky catalogs, the position of the
Galactic plane can be revised and updated definitions of the Galactic
coordinate systems can be proposed. We re-determine the position of the
Galactic plane based on modern large catalogs, such as the Two Micron All-Sky
Survey (2MASS) and the SPECFIND v2.0. This paper also aims to propose a
possible definition of the optimal Galactic coordinate system by adopting the
ICRS position of the Sgr A* at the Galactic center. The near-infrared 2MASS
point source catalog and the SPECFIND v2.0 catalog of radio continuum spectra
are used to determine the mean position of the Galactic plane on the celestial
sphere. By fitting the data to an ideal Galactic equator, the parameters
defining the Galactic coordinate system are obtained. We find that the
obliquity of the Galactic equator on the ICRS principal plane is about
$0.4^\circ$ (2MASS) and $0.6^\circ$ (SPECFIND v2.0) larger than the J2000.0
value, which is widely used in coordinate transformations between the
equatorial $(\alpha, \delta)$ and the Galactic $(\ell, b)$. Depending on the
adopted parameters, data, and methods, the largest difference between the
resulting Galactic coordinate systems is several arcminutes. We derive revised
transformation matrices and parameters describing the orientation of the
Galactic coordinate systems in the ICRS at the 1 milli-arcsecond level to match
the precision of modern observations. For practical applications, we propose
that a revised definition of the Galactic coordinate system should be required
in the near future.
