The growth of a magnetic field in a given random flow of a well-conducting liquid is considered. The known Lagrange solution for the transport of a frozen-in magnetic field is utilized. Magnetic diffusion is taken into account by averaging the result of this transport over a set of random trajectories. This permits a derivation of the equations for the mean magnetic field and its moments, as well as an investigation of the true (random) magnetic field. The field and its moments increase exponentially in the limit of large magnetic Reynolds numbers, and the field distribution becomes intermittent. The analysis is devoted mainly to streams that are restored after a definite time interval, but stationary flows with stochastic properties are also discussed.