In this paper we compute the rank and exhibit a presentation for the monoids

of all $P$-stable and $P$-order preserving partial permutations on a finite set

$\Omega$, with $P$ an ordered uniform partition of $\Omega$. These (inverse)

semigroups constitute a natural class of generators of the pseudovariety of

inverse semigroups ${\sf NO}$ of all normally ordered (finite) inverse

semigroups.