  A finite family of $R_I$ polynomials is introduced and studied. It consists
in a set of polynomials of $_{3}F_{2}$ form whose biorthogonality to an
ensemble of rational functions is spelled out. These polynomials are shown to
satisfy two generalized eigenvalue problems: in addition to their recurrence
relation of $R_I$ type, they are also found to obey a difference equation.
Underscoring this bispectrality is a triplet of operators with tridiagonal
actions.
