[en] The gross theory of beta-decay has been developed, and this theory offers the means of calculating directly the function of beta-decay intensity, then half-lives, complex beta spectra and so on are estimated from it. This paper presents the more refined theory by introducing the shell effect. The shell effect is considered in the intensity function. The half-lives in the electron decay of In with spin of 9/2⁺, the positron decay of Bi, Po, At and Rn, and the decay of odd-odd nuclei were estimated. The introduction of the shell effect shows better agreement between the theory and the experimental data. The inequality relations of intensity functions and half-lives of two adjacent nuclei were obtained. When the spins and parities of two nuclei are same, the inequality relations hold especially good. (Kato, T.)