  We present new measurements about the tunneling conductance in the
borocarbide superconductor TmNi$_2$B$_2$C. The results show a very good
agreement with weak coupling BCS theory, without any lifetime broadening
parameter, over the whole sample surface. We detect no particular change of the
tunneling spectroscopy below 1.5K, when both the antiferromagnetic (AF) phase
and the superconducting order coexist.
