Pareto set and Edgeworth box General equilibrium framework; two individuals, two goods represented in an Edgeworth box.

Is it true that if the preference are both strongly monotonic the Pareto set will go from the origin of an individual's axis to the one of the other's axis? By origin, I mean the points of the box where an individual has everything and the other nothing. The reason would be that the allocation of all goods to one of the single individuals is Pareto optimal.
The Pareto optimal set should always pass through the origin because it's one of the point that makes it impossible to better off a consumer without harming the other.