  The jet function for the factorized cross section $e^+e^-$ into dijets is
given as a function of the jet invariant mass s and with a generic jet
algorithm at $\mathcal{O}(\alpha_s)$. We demonstrate the results using the
Sterman-Weinberg algorithm and show that the jet function is independent of the
energy fraction $\beta$ of the soft radiation. The anomalous dimension has the
same form with and without the cone half-angle $\delta$. The dependence of the
finite part of the jet function on the cone angle is given.
