The phase structure of a gauge-scalar (Higgs) field system is studied by Monte Carlo simulations without freezing the radial mode of the scalar field. We consider Z 2 lattice gauge theory coupled to a Higgs field which is approximated by a discrete real one. Most of our analysis is done on a 4 4 lattice. We find that the phase diagram of our model consists of three distinct phases, Higgs and confined regions being divided by a phase boundary. This phase structure forms a contrast with that presented in the model with a fixed-length Higgs field.