  By using a generalization of Sturm-Liouville problems in $q$-difference
spaces, a class of symmetric $q$-orthogonal polynomials with four free
parameters is introduced. The standard properties of these polynomials, such as
a second order $q$-difference equation, the explicit form of the polynomials in
terms of basic hypergeometric series, a three term recurrence relation and a
general orthogonality relation are presented. Some particular examples are then
studied in detail.
