  We provide a congruence theorem for minimal surfaces in $S^5$ with constant
contact angle using Gauss-Codazzi-Ricci equations. More precisely, we prove
that Gauss-Codazzi-Ricci equations for minimal surfaces in $S^5$ with constant
contact angle satisfy an equation for the Laplacian of the holomorphic angle.
Also, we will give a characterization of flat minimal surfaces in $S^5$ with
constant contact angle.
