In the traditional theory of β-decay, the radial parts of the eigenfunctions of the electron which are divided by rl (l#x2019;s are orbital angular momenta) are put out of the integral symbols replacing r by ⍴ (nuclear radius), and the remaining integrals are arranged as nuclear matrix elements. In the presence of the Coulomb field, however, some of them deviate from constants appreciably in the nucleus, and it is hard to put them out of the integrals. In this paper the correction factors which include these eigenfunctions in the integral symbols are given, and it is discussed how much difference from the old theory is produced.