Like temporal instability, spatial instability also plays an important role for the development and evolution of disturbances in geophysical fluids. Based on the normal mode method, the spatial instability of the barotropic geostrophic flow for is investigated. The necessary condition for spatial instability of a barotropic geostrophic base flow with respect to a given small disturbances is the partial differential quotient of the potential vorticity of the base flow with respect to the latitude has the same sign as that of the phase velocity of the disturbance. Under certain conditions, like the classical temporal instability theory, the same criteria as the necessary conditions are provided, namely the Rayleigh-Kuo theorem and the Fj\o rtoft theorem.