  We have studied the magnetic-field-tuned superconductivity destroying quantum
transition in amorphous In-O films with the onset of superconductivity in zero
field at about 2 K. At temperatures down to 30 mK the critical resistance
R_c=R(T,B_c) has been found to change approximately linearly with temperature,
which is in contradiction to a standard description where zero slope dR_c/dT =
0 is assumed near T=0. To make the data R(T,B) collapse in the vicinity of
transition against scaling variable (B-B_c)/T^{1/y}, one has either to allow
for the intrinsic temperature dependence of R_c or to postulate the critical
field B_c to be temperature-dependent B_c(T)-B_c(0)~T^{1+1/y}. We find that the
state on the high-field side of the transition can be both insulating and
metallic and we determine the critical index y=1.2.
