  It is well known that a majorana mass induces a (small) transition magnetic
moment. The converse is also true; in this paper we estimate the loop
contribution of transition magnetic moments $[\mu]_{\alpha \beta}$ to the
neutrino mass matrix $[m]_{\alpha \beta}$. We show that for hierarchical
neutrino masses, the contribution of $[\mu]_{e \tau}$ to $[m]_{e \tau}$ can
exceed the experimental value of $[m]_{e \tau}$.
