  This paper discusses the location of zeros of polynomials in a polynomial
sequence $\{P_n(z)\}$ generated by a three-term recurrence relation of the form
$P_n(z)+ B(z)P_{n-1}(z) +A(z) P_{n-k}(z)=0$ with $k>2$ and the standard initial
conditions $P_{0}(z)=1, P_{-1}(z)=\ldots=P_{-k+1}(z)=0,$ where $A(z)$ and
$B(z)$ are arbitrary coprime real polynomials. We show that there always exist
polynomials in $\{P_n(z)\}$ with non-real zeros.
