ABSTRACT The recently discovered binary LB-1 has been reported to contain a ${∼ }70\, \mathrm{M}_{⊙}$ black hole (BH). The evidence for the unprecedentedly high mass of the unseen companion comes from reported radial velocity (RV) variability of the H α emission line, which has been proposed to originate from an accretion disc around a BH. We show that there is in fact no evidence for RV variability of the H α emission line, and that its apparent shifts instead originate from shifts in the luminous star’s H α absorption line. If not accounted for, such shifts will cause a stationary emission line to appear to shift in antiphase with the luminous star. We show that once the template spectrum of a B star is subtracted from the observed Keck/HIRES spectra of LB-1, evidence for RV variability vanishes. Indeed, the data rule out periodic variability of the line with velocity semi-amplitude $K_{\rm H\,α } \gt 1.3\, {\rm {km}} \, s^{-1}$. This strongly suggests that the observed H α emission does not originate primarily from an accretion disc around a BH, and thus that the mass ratio cannot be constrained from the relative velocity amplitudes of the emission and absorption lines. The nature of the unseen companion remains uncertain, but a ‘normal’ stellar-mass BH with mass 5 ≲ M/M⊙ ≲ 20 seems most plausible. The H α emission likely originates primarily from circumbinary material, not from either component of the binary.