  Let $ \beta $ be a real number less than -1. In this paper, we prove the
uniqueness of the measure with maximal entropy of the negative $\beta$-shift.
Endowed with the shift, this symbolic dynamical system is coded under certain
conditions, but in all cases, it is shown that the measure with maximal entropy
is carried by a support coded by a recurrent positive code. One of the
difference between the positive and the negative $\beta$-shift is the existence
of gaps in the system for certain negative values of $ \beta $ . These are
intervals of negative $\beta$-representations (cylinders) negligible with
respect to the measure with maximal entropy, which is a measure of Champernown.
