  We prove here that in the Theorem on Local Ergodicity for Semi-Dispersive
Billiards (proved by N. I. Chernov and Ya. G. Sinai in 1987) the recently added
condition (by P. B\'alint, N. Chernov, D. Sz\'asz, and I. P. T\'oth, in order
to save this fundamental result) on the algebraic character of the smooth
boundary components of the configuration space is unnecessary. Having saved the
theorem in its original form by using additional ideas in the spirit of the
initial proof, the result becomes stronger and it applies to a larger family of
models.
