  A natural generalization of interval exchange maps are linear involutions,
first introduced by Danthony and Nogueira. Recurrent train tracks with a single
switch provide a subclass of linear involutions. We call such linear
involutions non-classical interval exchanges. They are related to measured
foliations on orientable flat surfaces.
  Non-classical interval exchanges can be studied as a dynamical system by
considering Rauzy induction in this context. This gives a refinement process on
the parameter space similar to Kerckhoff's simplicial systems. We show that the
refinement process gives an expansion that has a key dynamical property called
{\it uniform distortion}. We use uniform distortion to prove normality of the
expansion. Consequently, we prove an analog of Keane's conjecture: almost every
non-classical interval exchange is uniquely ergodic. Uniform distortion has
been independently shown by Avila-Resende.
