  Nucleon-nucleon scattering in the $^1S_0$ partial wave is considered in
chiral effective field theory within the renormalizable formulation of Ref. [1]
beyond the leading-order approximation. By applying subtractive
renormalization, the subleading contact interaction in this channel is taken
into account non-perturbatively. For a proper choice of renormalization
conditions, the predicted energy dependence of the phase shift and the
coefficients in the effective range expansion are found to be in a good
agreement with the results of the Nijmegen partial wave analysis.
