  We find the possibility of the non-perturbative an-harmonic correction to
Mehler's formula for propagator of the harmonic oscillator. We evaluate the
conditional Wiener measure functional integral with a term of the fourth order
in the exponent by an alternative method as in the conventional perturbative
approach. In contrast to the conventional perturbation theory, we expand into
power series the term linear in the integration variable in the exponent. We
discuss the case, when the starting point of the propagator is zero. We present
the results in analytical form for positive and negative frequency.
