  It is elementary and well-known that if an element x of a bounded modular
lattice L has a complement in L then x has a relative complement in every
interval [a,b] containing x. We show that the relatively strong assumption of
modularity of L can be replaced by a weaker one formulated in the language of
so-called modular triples. We further show that, in general, we need not
suppose that x has a complement in L. By introducing the concept of modular
triples in posets, we extend our results obtained for lattices to posets. It
should be remarked that the notion of a complement can be introduced also in
posets that are not bounded.
