Using the monomer-dimer representation of the lattice Schwinger model, with N_f =1 Wilson fermions in the strong-coupling regime (beta=0), we evaluate its partition function, Z, exactly on finite lattices. By studying the zeroes of Z(k) in the complex plane (Re(k),Im(k)) for a large number of small lattices, we find the zeroes closest to the real axis for infinite stripes in temporal direction and spatial extent S=2 and 3. We find evidence for the existence of a critical value for the hopping parameter in the thermodynamic limit S going to infinity on the real axis at about k_c = 0.39. By looking at the behaviour of quantities, such as the chiral condensate, the chiral susceptibility and the third derivative of Z with respect to 1/2k, close to the critical point k_c, we find some indications for a continuous phase transition.