We examine whether or not double white dwarfs are ultimately merging into one body. It has been argued that such a double white dwarf system forms from some intermediate-mass binary stars and will merge due to the gravitational radiation which decreases the separation of binary. After filling the inner critical Roche lobe, the less massive component begins to transfer its mass to the more massive one. When the mass transfer rate exceeds a some critical value, a common envelope is formed. If the common envelope is hydrostatic, the mass transfer is tuned up to be a some value which depends only on the white dwarf mass, radius, and the Roche lobe size. The mass transfer from the less massive to the more massive components leads the separation to increase. On the other hand, the gravitational radiation effect reduces the separation. Which effect wins determines the fate of double white dwarfs, that is, whether merging or not merging. Since the formula of the gravitational radiation effect is well known, we have studied the mass accretion rate in common envelope phase of double white dwarfs assuming the Roche lobe size is as small as 0.03 R⊙ or 0.1 R⊙.