  We study Schwarz's map for Appell's second system $\cF_2$ of hypergeometric
differential equations in two variables with parameters
$a=c_1=c_2=\frac{1}{2}$, $b_1=b_2=\frac{1}{4}$. By using theta functions with
characteristics, we give a defining equation of an analytic set in $\C^2\times
\H$ of its image, and express its inverse.
