We proved that every subshift factor of ($-\beta$) shifts is intrinsically ergodic, when $\beta$ is more than the golden ratio and the ($-\beta$)-expansion of $-1$ is not periodic with odd period. Moreover, the unique measure of maximal entropy satisfies a certain Gibbs property. This is an application of the technique established by Climenhaga and Thompson to prove intrinsic ergodicity beyond specification. We also prove that there exists a factor of $(-\beta)$-shift which is not intrinsically ergodic in the cases other than the above. This is a joint work with Kenichiro Yamamoto in Nagaoka University of Technology.