  We extend the high-temperature series of the free energy for the XY model in
two dimensions to order $\beta^{48}$ from the previous order of $\beta^{22}$ by
applying the improved algorithm of the finite lattice method. The long series
obtained enables us to conclude that the behavior of the free energy is
consistent in high accuracy with what is expected when the phase transition of
the model is of the Kosterlitz-Thouless type .
