The heaviness of the top quark makes its two-body Cabibbo-favored decay mode $t\ensuremath{\rightarrow}b{W}^{+}$ to be dominant, at such a level that hardly any other decay mode reaches a detectable branching ratio within the Standard Model. Here we study the decay $t\ensuremath{\rightarrow}b{W}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}$ ($\ensuremath{\ell}=e,\ensuremath{\mu},\ensuremath{\tau}$), which diverges for massless leptons, and it can reach a branching ratio $\ensuremath{\sim}\mathcal{O}(1{0}^{\ensuremath{-}5}\ensuremath{\sim}1{0}^{\ensuremath{-}6})$ for reasonable values of the low energy cut in the lepton pair invariant mass. This rate surpasses almost any other rare decays such as $t\ensuremath{\rightarrow}cX$ ($X=\ensuremath{\gamma},Z,g,H,{W}^{+}{W}^{\ensuremath{-}}$), and thus offers the possibility of being detectable. Furthermore, the estimate of this channel is relevant because it can mimic the signal arising from the lepton number violating decay $t\ensuremath{\rightarrow}b{W}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{+}$, when the $W$ boson decays into lepton channels.