A class of functional integrals with nonquadratic argument of the exponential is considered and a solution obtained in the form of a series in a parameter $b$ that is small, whereas the parameter of standard perturbation theory is large. It is very important that the series converges for all $b>0$. The method makes it possible to solve, for example, the well-known problem of wave propagation in a randomly inhomogeneous medium, and it may also be helpful for numerous other problems.