  Determination of the accurate astrophysical S factor of
{$^{12}$C($\alpha,\gamma$)$^{16}$O} reaction has been regarded as a holy grail
of nuclear astrophysics for decades. In current stellar models, a knowledge of
that value to better than 10\% is desirable. Due to the practical issues,
tremendous experimental and theoretical efforts over nearly 50 years are not
able to reach this goal, and the published values contradicted with each other
strongly and their uncertainties are 2 times larger than the required
precision. To this end we have developed a Reduced R-matrix Theory, based on
the classical R-matrix theory of Lane and Thomas, which treats primary
transitions to ground state and four bound states as the independent reaction
channels in the channel spin representation. With the coordination of
covariance statistics and error propagation theory, a global fitting for almost
all available experimental data of $^{16}$O system has been multi-iteratively
analyzed by our powerful code. A reliable, accurate and self-consistent
astrophysical S factor of {$^{12}$C($\alpha,\gamma$)$^{16}$O} was obtained with
a recommended value $S_{tot}$ (300) = 162.7 $\pm$ 7.3 keV b (4.5\%) which could
meet the required precision.
