It is known that the conditional distribution density \[ f(t,x,\tau ,\xi ) = \frac{1}{{2\sqrt {\pi (\tau - t)} }}\exp \left[ { - \frac{{(\xi - x)^2 }}{{4(\tau - t)}}} \right] \] is a solution to the differential equation ${f_t} ^\prime + {f_{xx}} ^{\prime \prime } = 0$ and determines a continuous Markov process. In the general case a Markov process of the diffusion type is described by Kolmogorov’s differential equation. The purpose of this paper is to transform a continuous process of the diffusion type into a process with the above-mentioned distribution. This transformation exists if $\Delta = 0$, where $\Delta $ is some determinant composed of coefficients $a(t,x)$ and $b(t,x)$ of Kolmogorov’s equation. Finally, examples of processes are given to which the theorem proved herein can be applied.