  Using the finite size scaling theory, we re-examine the nature of the bulk
phase transition in the fundamental-adjoint coupling plane of the SU(2) lattice
gauge theory at $\beta_A = 1.25$ where previous finite size scaling
investigations of the deconfinement phase transition showed it to be of first
order for temporal lattices with four sites. Our simulations on $N^4$ lattices
with N=6, 8, 10, 12 and 16 show an absence of a first order bulk phase
transition. We find the discontinuity in the average plaquette to decrease
approximately linearly with $N$. Correspondingly, the plaquette susceptibility
grows a lot slower with the 4-volume of the lattice than expected from a first
order bulk phase transition.
