  Let $ l : \Sigma \to X$ be a weakly Lagrangian map of a compact orientable
surface $ \Sigma$ in a K\"ahler surface $ X$ which is area minimizing in its
homotopy class of maps in $ W^{1,2}(\Sigma, X)$, the Sobolev space of maps of
square integrable first derivative. Schoen and Wolfson showed such $ l$ is
Lipschitz, and it is smooth except at most at finitely many points of Maslov
index 1 or -1. In this note, we observe if in addition c_1(X)[l]=0, $ l$ is
smooth everywhere. Here $ c_1(X)$ is the first Chern class of $ X$.
