  We report the first experimental observation of parametric generation of
second sound (SS) by first sound (FS) in superfluid helium in a narrow
temperature range in the vicinity of $T_\lambda $. The temperature dependence
of the threshold FS amplitude is found to be in a good quantitative agreement
with the theory suggested long time ago and corrected for a finite geometry.
Strong amplitude fluctuations and two types of the SS spectra are observed
above the bifurcation. The latter effect is quantitatively explained by the
discreteness of the wave vector space and the strong temperature dependence of
the SS dissipation length.
