  We show that the standard Skyrme model without pion mass term can be
expressed as a sum of two BPS submodels, i.e., of two models whose static field
equations, independently, can be reduced to first order equations. Further,
these first order (BPS) equations have nontrivial solutions, at least locally.
These two submodels, however, cannot have common solutions. Our findings also
shed some light on the rational map approximation. Finally, we consider certain
generalisations of the BPS submodels.
