  We investigate orthonormality-preserving, C*-conformal and conformal module
mappings on Hilbert C*-modules to obtain their general structure.
Orthogonality-preserving bounded module maps T act as a multiplication by an
element \lambda of the center of the multiplier algebra of the C*-algebra of
coefficients combined with an isometric module operator as long as some polar
decomposition conditions for the specific element \lambda are fulfilled inside
that multiplier algebra. Generally, T always fulfils the equality $<T(x),T(y) >
= | \lambda |^2 < x,y>$ for any elements x,y of the Hilbert C*-module. At the
contrary, C*-conformal and conformal bounded C*-linear mappings are shown to be
only the positive real multiples of isometric module operators.
