  Free quadratic harness is a Markov process from the class of quadratic
harnesses, i.e. processes with linear regressions and quadratic conditional
variances. The process has recently been constructed for a restricted range of
parameters in the paper "Askey-Wilson polynomials, quadratic harnesses and
martingales" by W. Bryc and J. Weso{\l}owski using Askey--Wilson polynomials.
Here we provide a self-contained construction of the free quadratic harness for
all values of parameters.
