  In this paper, we study representations of real numbers in the positional
numeration system with negative basis, as introduced by Ito and Sadahiro. We
focus on the set $\Z_{-\beta}$ of numbers whose representation uses only
non-negative powers of $-\beta$, the so-called $(-\beta)$-integers. We describe
the distances between consecutive elements of $\Z_{-\beta}$. In case that this
set is non-trivial we associate to $\beta$ an infinite word
$\boldsymbol{v}_{-\beta}$ over an (in general infinite) alphabet. The
self-similarity of $\Z_{-\beta}$, i.e., the property $-\beta \Z_{-\beta}\subset
\Z_{-\beta}$, allows us to find a morphism under which
$\boldsymbol{v}_{-\beta}$ is invariant. On the example of two cubic irrational
bases $\beta$ we demonstrate the difference between Rauzy fractals generated by
$(-\beta)$-integers and by $\beta$-integers.
