More than 400 $K^{+}topi^{+}mu^+mu^-$ events were observed in a rare $K^+$ decay experiment at the AGS. Normalized to the $K^{+}topi^{+}pi^+pi^-$ decay, the branching ratio is determined to be $(9.22 pm 0.60 (stat) pm 0.49 (syst))times 10^{-8}$. This branching ratio and the $mumu$ mass spectrum is in very good agreement with the measurement of the $K^{+}topi^{+}e^+e^-$ decay, but deviates significantly from the previous measurement.