  We calculate the high-temperature series of the magnetic susceptibility and
the second and fourth moments of the correlation function for the XY model on
the square lattice to order $\beta^{33}$ by applying the improved algorithm of
the finite lattice method. The long series allow us to estimate the inverse
critical temperature as $\beta_c=1.1200(1)$, which is consistent with the most
precise value given previously by the Monte Carlo simulation. The critical
exponent for the multiplicative logarithmic correction is evaluated to be
$\theta=0.054(10)$, which is consistent with the renormalization group
prediction of $\theta={1/16}$.
