  [Abridged] We have produced a cleaned map of the Wilkinson Microwave
Anisotropy Probe (WMAP) 3-year data using an improved foreground subtraction
technique. We perform an internal linear combination (ILC) to subtract the
Galactic foreground emission from the temperature fluctuations observed by the
WMAP. We divide the whole sky into hundreds of pixel groups with similar
foreground spectral indices over a range of WMAP frequencies, apply the ILC for
each group, and obtain a CMB map with foreground emission effectively reduced.
With the resulting foreground-reduced ILC map, we have investigated the known
anomalies in CMB maps at large scales. The quadrupole and the octopole powers
measured from our ILC map are \delta T_2^2 = 276_{-126}^{+94} uK^2 and \delta
T_3^2 = 952_{-83}^{+64} uK^2, respectively. The measured quadrupole power is
lower than the value expected in the concordance LCDM model (1250 uK^2), in
which the probability of finding a quadrupole power lower than the measured
value is 5.7%. We have confirmed that the quadrupole and the octopole are
strongly aligned with angle \theta_{23} = 11.8_{-8.0}^{+6.4} degree, and are
planar with high planarity parameters t=0.98_{-0.02}^{+0.02} for l=2 and
t=0.91_{-0.03}^{+0.02} for l=3. The observed angular separation \theta_{23} is
marginally statistically significant because the probability of finding the
angular separation as low as the observed value is 4.3%. However, the observed
planarity is not statistically significant. The probability of observing such a
planarity as high as the measured t values is over 18%. The ILC simulations
show that the residual foreground emission in the ILC map does not affect the
estimated values significantly.
