  In this paper, two new composition operations are defined among the
order-preserving maps. They can act on order-preserving maps like the usual
composition operation. They are coincide with the usual composition operation
when the order-preserving maps are sup-preserving maps or meet-preserving maps.
The usual composition operation can't endow the set $L^{L}$ of order preserving
maps on a complete lattices $L$ with quantale or co-quantale structures.
Luckily, two new operations can endow $L^{L}$ with a quantale and a co-quantale
structures respectively, whenever $L$ is a completely distributive lattice.
