A generalized linear dispersion relation of electromagnetic slab universal modes is derived, taking into account arbitrary ion charge state, electron finite Larmor radius (FLR) effects, and Debye shielding effects. As a consequence, it provides more accurate predictions and is applicable to a wider range of plasmas. We find that electron FLR effects have a weakly stabilizing effect on the slab universal instability in electron-ion plasma, while Debye shielding strongly stabilizes this instability when λ D approaches ρ i (λ D is the Debye length and ρ i is the ion gyro-radius). In particular, we examine the stability criterion for this instability in electron-positron pair plasmas, and find that the instability persists in this simplest plasma system as long as the pair plasma number density exceeds the critical value n c = B 2 /(8πm e c 2 ).