We  construct  a  map  on  the   space   of   interval   exchange
transformations, which  generalizes  the  classical  map  on  the
interval,  related  to continued fraction expansion. This map  is
based on  Rauzy induction, but unlike  its relatives known  up to
now, the  map is ergodic with  respect to some  finite absolutely
continuous  measure   on   the   space   of   interval   exchange
transformations. We  present  the prescription for calculation of
this measure based on technique  developed  by  W.Veech for Rauzy
induction.

We study Lyapunov  exponents related to  this map and  show  that
when  the   number  of  intervals   is  $m$,  and  the  genus  of
corresponding  surface   is   $g$,   there  are  $m-2g$  Lyapunov
exponents, which are equal to zero, while the remaining $2g$ ones
are distributed into pairs:
          exponent number i  = -(exponent number m-i+1)
We present an explicit formula for the largest one.