  We show that a Majorana fermion description of the two channel Kondo model
can emerge quite naturally as a representation of the algebra associated with
the spin currents in the two channels. Using this representation we derive an
exact equivalent Hamiltonian for the two channel model expressed entirely in
terms of Majorana fermions. The part of the Hamiltonian that is coupled to the
impurity spin corresponds to the vector part of the $\sigma$-$\tau$ model
(compactified two channel model). Consequently all the thermodynamic properties
associated with the impurity spin can be calculated from the $\sigma$-$\tau$
model alone. The equivalent model can be used to confirm the interpretation of
the many-body excitation spectrum of the low energy fixed point of the
two-channel model as due to free Majorana fermions with appropriate boundary
conditions.
