It has been suggested that the current convective instability may be responsible for the structuring, i.e., generation of density irregularities, of density enhancements (known as ''blobs'') in the auroral ionosphere. However, previous theories have neglected the finite extent of the ''blob'' along the geomagnetic field. In this paper we develop a nonlocal theory of the current convective instability which considers the finite extent of an ionospheric ''blob'' parallel to the geomagnetic field. We find that the growth rate of the instability can be substantially reduced in the finite-sized ''blob'' case from the value obtained in the local approximation for an infinitely long blob. For auroral ionosphere parameters, the reduction in the growth rate for medium-scale irregularities (1--10 km) can be 1 to 2 orders of magnitude for the typical observed values of ''blob'' sizes (approximately a few hundred kilometers). Thus is appears that the current convective instability is not a viable mechanism to generate scintillation causing irregularities, i. e., 1- to 10-km irregularities.