  We consider the double sinh-Gordon potential which is a quasi-exactly
solvable problem and show that in this case one has two sets of Bender-Dunne
orthogonal polynomials . We study in some detail the various properties of
these polynomials and the corresponding quotient polynomials. In particular, we
show that the weight functions for these polynomials are not always positive.
We also study the orthogonal polynomials of the double sine-Gordon potential
which is related to the double sinh-Gordon case by an anti-isospectral
transformation. Finally we discover a new quasi-exactly solvable problem by
making use of the anti-isospectral transformation.
