  The general theory of N=1 supergravity with supermatter is applied to a
Bianchi type IX diagonal model. The supermatter is constituted by a complex
scalar field and its spin-$1\over 2$ fermionic partners. The K\"ahler geometry
is chosen to be a two-dimensional flat one. The Lorentz invariant Ansatz for
the wave function of the universe is taken to be as simple as possible in order
to obtain {\it new} solutions. The set of differential equations derived from
the quantum constraints are analysed in two different cases: if the supermatter
terms include an analytical potential or not. In the latter the wave function
is found to have a simple form.
