In this paper, we study representations of real numbers in the positional
numeration system with negative basis, as introduced by Ito and Sadahiro. We
introduce an analogue of the greedy algorithm for obtaining these
representations. We describe the distances between consecutive elements of the
set $\Z_{-\beta}$ of numbers whose representation uses only non-negative powers
of $-\beta$, the so-called $(-\beta)$-integers.