  A special class of orthogonal rational functions (ORFs) is presented in this
paper. Starting with a sequence of ORFs and the corresponding rational
functions of the second kind, we define a new sequence as a linear combination
of the previous ones, the coefficients of this linear combination being
self-reciprocal rational functions. We show that, under very general conditions
on the self-reciprocal coefficients, this new sequence satisfies orthogonality
conditions as well as a recurrence relation. Further, we identify the
Caratheodory function of the corresponding orthogonality measure in terms of
such self-reciprocal coefficients.
  The new class under study includes the associated rational functions as a
particular case. As a consequence of the previous general analysis, we obtain
explicit representations for the associated rational functions of arbitrary
order, as well as for the related Caratheodory function. Such representations
are used to find new properties of the associated rational functions.
