  We improve the sphaleron decoupling condition in the real singlet-extended
standard model. The sphaleron energy is obtained using the finite temperature
one-loop effective potential with daisy resummation. For moderate values of the
model parameters, the sphaleron decoupling condition is found to be
$v_C/T_C>(1.1-1.2)$, where $T_C$ denotes a critical temperature and $v_C$ is
the corresponding vacuum expectation value of the doublet Higgs field at $T_C$.
We also investigate the deviation of the triple Higgs boson coupling from its
standard model value in the region where the improved sphaleron decoupling
condition is satisfied. As a result of the improvement, the deviation of the
triple Higgs boson coupling gets more enhanced. In a typical case, if the Higgs
couplings to the gauge bosons/fermions deviate from the SM values by about 3
(10)%, the deviation of the triple Higgs boson coupling can be as large as
about 16 (50)%, which is about 4 (8)% larger than that based on the
conventional criterion $v_C/T_C>1$.
