An electrostatic ion cyclotron instability driven by sheared velocity flow perpendicular to a uniform magnetic field is investigated in the local approximation. The dispersion equation, which includes all kinetic effects and involves only one important parameter, is cast in the form of Gordeyev integrals and solved numerically. The instability occurs roughly at multiples of the ion cyclotron frequency (but modified by the shear) with the growth rate of the individual harmonics overlapping in wavenumber. At small values of the shear parameter, the instability exists in two branches, one at long wavelength, k&rgr;i~0.5, and one at short wavelength, k&rgr;i>1.5 (k&rgr;i is the wavenumber normalized to the ion gyroradius). At larger values of the shear parameter only the longer wavelength branch persists. The growth rate of the long wavelength mode, maximized over wavenumber and frequency, increases monotonically with the shear parameter. Properties of the instability are compared to those of Ganguli et al. (1985b, 1988b) obtained in the nonlocal limit. ¿ American Geophysical Union 1992