We demonstrate that the universal mode driven by the density gradient in a plasma slab can be absolutely unstable even in the presence of reasonable magnetic shear. Previous studies from the 1970s that reached the opposite conclusion used an eigenmode equation limited to L_{x}≫ρ_{i}, where L_{x} is the scale length of the mode in the radial direction, and ρ_{i} is the ion Larmor radius. Here we instead use a gyrokinetic approach which does not have this same limitation. Instability is found for perpendicular wave numbers k_{y} in the range 0.7≲k_{y}ρ_{i}≲100, and for sufficiently weak magnetic shear: L_{s}/L_{n}≳17, where L_{s} and L_{n} are the scale lengths of magnetic shear and density. Thus, the plasma drift wave in a sheared magnetic field may be unstable even with no temperature gradients, no trapped particles, and no magnetic curvature.