  In the past decades, determinants and Pfaffians were found for eigenvalue
correlations of various random matrix ensembles. These structures simplify the
average over a large number of ratios of characteristic polynomials to
integrations over one and two characteristic polynomials only. Up to now it was
thought that determinants occur for ensembles with Dyson index $\beta=2$
whereas Pfaffians only for ensembles with $\beta=1,4$. We derive a non-trivial
Pfaffian determinant for $\beta=2$ random matrix ensembles which is similar to
the one for $\beta=1,4$. Thus, it unveils a hidden universality of this
structure. We also give a general relation between the orthogonal polynomials
related to the determinantal structure and the skew-orthogonal polynomials
corresponding to the Pfaffian. As a particular example we consider the chiral
unitary ensembles in great detail.
