It is shown that the model proposed recently by M. H. Cohen is a gapless superconductor. The detailed analysis is made in the weak coupling limit. The specific heat is nearly linear and the thermodynamical critical field nearly quadratic in temperature. The model shows neither nonlinear nor Josephson tunneling. Yet the coefficient b in Cohen's gap parameter Δ(ε)=bε obeys Ginzburg-Landau equations, so that the model does show the Meissner effect and infinite d.c. conductivity. The shift of the transition point caused by non-magnetic impurities is also obtained to the first order of the impurity concentration.