  The fact that minimal surfaces in the four-dimensional Euclidean space admit
natural parameters implies that any minimal surface is determined uniquely up
to a motion by two curvature functions, satisfying a system of two PDE's (the
system of natural PDE's). In fact this solves the problem of Lund-Regge for
minimal surfaces. Using the corresponding result for minimal surfaces in the
three-dimensional Euclidean space, we solve explicitly the system of natural
PDE's, expressing any solution by virtue of two holomorphic functions in the
Gauss plane. We find the relation between two pairs of holomorphic functions
(i.e. the class of pairs of holomorphic functions) generating one and the same
solution of the system of natural PDE's.
