  An exact solution to the problem of parametric level statistics in
non-Gaussian ensembles of N by N Hermitian random matrices with either soft or
strong level confinement is formulated within the framework of the orthogonal
polynomial technique. Being applied to random matrices with strong level
confinement, the solution obtained leads to emergence of a new connection
relation that makes a link between the parametric level statistics and the
scalar two-point kernel in the thermodynamic limit.
