  Pairing symmetry in $\kappa$-(BEDT-TTF)$_2$X is re-examined by applying
fluctuation exchange method to the Hubbard model on the original four band
lattice for the first time. Our study is motivated by the discrepancy between a
recent thermal conductivity/tunneling spectroscopy experiments and the previous
theories based on the effective single or two band model. In contrast to the
previous theories, we find that $d_{x^2-y^2}$-like pairing dominates over
$d_{xy}$ in agreement with recent experiments. Our study provides a general
lesson that even if the Fermi surface seems to be reproduced by an effective
model, the pairing symmetry can be different from that of the original system.
