Beauty production in events containing two final-state muons has been measured with the ZEUS detector at HERA using an
integrated luminosity of 377 pb$^{-1}$. A low transverse-momentum threshold for muon identification, together with the large rapidity coverage of the ZEUS muon system and the upgraded ZEUS tracker, give access to an almost full phase space for beauty production in this channel. The cross section for beauty production in $ep$ collisions has been measured to be $11.4\pm0.8$ (stat.) $^{+3.9}_{-3.4}$ (syst.) nb. Differential cross sections and $b\bar{b}$ correlations are compared to previous measurements and theoretical models.