  A set of $m$ distinct nonzero rationals $\{a_1, a_2,\ldots, a_m\}$ such that
$a_i a_j+1$ is a perfect square for all $1\le i <j \le m$, is called a rational
Diophantine $m$-tuple. If in addition, $a_i^2+1$ is a perfect square for $1\le
i\le m$, then we say the $m$-tuple is strong. In this paper, we construct
infinite families of rational Diophantine sextuples containing a strong
Diophantine pair.
