  We show that the normalised ultraspherical polynomials,
$G_n^{(\lambda)}(x)=C_n^{(\lambda)}(x)/C_n^{(\lambda)}(1)$, satisfy the
following stronger version of Tur\'{a}n inequality, $$|x|^\theta
\left(G_n^{(\lambda)}(x)\right)^2 -G_{n-1}^{(\lambda)}(x)G_{n+1}^{(\lambda)}(x)
\ge 0 ,\;\;\;|x| \le 1, $$ where $\theta=4/(2-\lambda)$ if $-1/2 <\lambda \le
0$, and $\theta=2/(1+2\lambda)$ if $\lambda \ge 0$. We also provide a similar
generalisation of Tur\'{a}n inequalities for some symmetric orthogonal
polynomials with a finite or infinite support defined by a three term
recurrence.
