  A set of $m$ distinct nonzero rationals $\{a_1,a_2,\ldots,a_m\}$ such that
$a_ia_j+1$ is a perfect square for all $1\leq i<j\leq m$, is called a rational
Diophantine $m$-tuple. It is proved recently that there are infinitely many
rational Diophantine sextuples. In this paper, we construct infinite families
of rational Diophantine sextuples with special structure, namely the sextuples
containing quadruples and quintuples of certain type.
