  The electroweak unification group $ SU(2)_L\times SU(2)_R\times SU(2)_Y $ is
proposed for the charged lepton flavor violating decays of the muon ($\mu$) and
tau ($\tau$) leptons. The group $SU(2)_Y$ is in the lepton space. The
left-handed leptons and anti-leptons are assigned to the fundamental
representation $(2,2,\bar{2})$ of the semi-simple group. The gauge group
$SU(2)_Y$ is spontaneously broken to $U(1)_{Y_1}$, where $Y_1=-L=\pm1$ is the
hypercharge, by introducing a scalar multiplet $\Sigma$ which belongs to the
triplet representation 3 of the $SU(2)_Y$ and is singlet under $SU(2)_L\times
SU(2)_R$. At this stage charged vector bosons $Y^\pm$ of $SU(2)_Y$ which
mediate the lepton flavor violating decays acquire masses and are decoupled
with one Higgs scalar $H_\Sigma^0$. The residual group $SU(2)_L\times
SU(2)_R\times U(1)_{Y_1}$ has all the features of the left-right electroweak
unification group extensively studied in the literature. The probability for
lepton flavor violating decays is
$\left(\frac{\sin^2\theta_W}{1-2\sin^2\theta_W}\right)^2\left(\frac{m_{W_L}}{m_Y}\right)^4$.
