  We consider a family of four-dimensional non-linear sigma models based on an
O(5) symmetric group, whose fields take their values on the 4-sphere S4. An
SO(4)-subgroup of the model is gauged. The solutions of the model are
characterised by two distinct topological charges, the Chern-Pontryagin charge
of the gauge field and the degree of the map, i.e. the winding number, of the
S4 field. The one dimensional equations arising from the variation of the
action density subjected to spherical symmetry are integrated numerically.
Several properties of the solutions thus constructed are pointed out. The only
solution with unit Chern-Pontryagin charge are the usual BPST instantons with
zero S4 winding number, while solutions with unit S4 winding number have zero
Chern-Pontryagin charge.
