  In this paper we consider the polynomial sequence $(P_{n}^{\alpha,q}(x))$
that is orthogonal on $[-1,1]$ with respect to the weight function
$x^{2q+1}(1-x^{2})^{\alpha}(1-x), \alpha>-1, q\in \mathbb N$; we obtain the
coefficients of the tree-term recurrence relation (TTRR) by using a different
method from the one derived in \cite{kn:atia1}; we prove that the interlacing
property does not hold properly for $(P_n^{\alpha,q}(x))$; and we also prove
that, if $x_{n,n}^{\alpha+i,q+j}$ is the largest zero of
$P_{n}^{\alpha+i,q+j}(x)$, $\displaystyle x_{2n-2j,2n-2j}^{\alpha+j,q+j}<
x_{2n-2i,2n-2i}^{\alpha+i,q+i}, 0\leq i<j\leq n-1$.
