  In this paper, by considering a special case of the spacelike mean curvature
flow investigated by Li and Salavessa [6], we get a condition for the existence
of smooth solutions of the Dirichlet problem for the minimal surface equation
in arbitrary codimension. We also show that our condition is sharper than
Wang's in [13, Theorem 1.1] provided the hyperbolic angle $\theta$ of the
initial spacelike submanifold $M_{0}$ satisfies $\max_{M_{0}}{\rm
cosh}\theta>\sqrt{2}$.
