Do indifference curves representing perfect complements violate the non satiation assumption?

Perfect complements satisfy a related assumption of monotonicity (more of everything is better) but neither local nonsatiation (either more or less of anything is better) or strong monotonicity (more of anything is better). Note that in the common example of left shoe/right shoe, goods are not continuous (infinitely divisible), thus local nonsatiation may not even apply (a change can't be an arbitrary constant but discrete).