  We investigate the phase structure of a four dimensional SO(4) invariant
lattice Higgs-Yukawa model comprising four reduced staggered fermions
interacting with a real scalar field. The fermions belong to the fundamental
representation of the symmetry group while the three scalar field components
transform in the self-dual representation of SO(4). We explore the phase
diagram and find evidence of a continuous transition between a phase where the
fermions are massless to one where the fermions acquire mass. This transition
is not associated with symmetry breaking and there is no obvious local order
parameter.
