A method for calculating the Lamb shift of an inner electron in a heavy atom is developed. This method contains only an expansion in $\alpha $, the coupling of the electron with the radiation field, but not in Z$\alpha $, where Z is the atomic number. Since the calculation is essentially non-covariant, care must be taken in eliminating divergent terms. A 'correct' finite part of the Lamb shift is obtained, and put into a form suitable for calculation. That this form is convenient will be demonstrated in the following paper where the Lamb shift of a K-electron in Hg is calculated.