  A numerical scaling analysis is used to show that Nagaoka's ferromagnetic
state in two-dimensional Hubbard model with one hole is supersede by an
antiferromagnetic (AF) state with a discontinuous jump in the total spin due to
the AF coupling as the Hubbard $U$ is made finite. The same applies to the
two-hole system, which has a spiral spin structure. We can show, via the
scaling, that the crossover to an AF state is a precursor of a pathological
coalescence of states having the minimum spin and Nagaoka's state at $U=\infty$
in the thermodynamic limit.
