  We present a model which supplements the Standard Electroweak Model with
three right-handed neutrinos and one extra scalar doublet which does not
develop a vacuum expectation value. With the aid of a discrete symmetry the
neutrinos are kept strictly massless. This model has several interesting
features. It has unsuppressed lepton flavour violating processes, in particular
$\mu \rightarrow e \gamma$, hinting at the possibility that these may soon be
within experimental reach. The $Z$ and $W$ interactions become non-diagonal at
one loop level. In particular, a non-trivial leptonic mixing matrix is seen to
arise from the clash between the charged gauge boson and the charged scalar
interactions.
