We present the relativistic version of the imaginary time method (ITM). The ionization probability w of the bound state under the action of electric and magnetic fields (for the case when the binding energy E b is comparable with mc 2 ) has been calculated using the ITM. The formulae obtained cover both the ionization of nonrelativistic bound systems (atoms, ions) and the case of E b = 2mc 2 , when w is compared with the probability of electron-positron pair production from vacuum in a strong field.