  The problem of determining completely the spin amplitudes of photoproduction
of two pseudoscalar mesons on a nucleon from observables is studied. The
procedure of reconstruction of the scattering matrix elements from a complete
set of observables is based on the expressions of all observables as quadratic
hermitean forms in the reaction matrix elements which are derived explicitly.
Their inversion allows one to find explicit solutions for the reaction matrix
elements in terms of observables. Two methods for finding a complete set of
observables are presented. In particular, one set was found, which does not
contain a triple polarization observable.
