We examine the instability of free convective boundary layer flows in porous media. The medium is bounded by two semi-infinite plane surfaces forming a wedge of angle a. One of the surfaces is heated uniformly and the other is either cold or insulated. The basic flow used in the analysis is the most accurate obtainable by means of higher order boundary layer theory. In general, the critical distance from the leading edge beyond which disturbances grow is found to be strongly dependent on the outer flow field. The only exception to this arises when the heated surface is close to the vertical and if the wedge is not too close to either 0 degrees or 360 degrees. The main implication of this paper is that instability occurs too close to the leading edge for the basic flow to be represented adequately either by the leading order boundary layer theory used in previous papers, or by even the most accurate higher order theory obtained using matched asymptotic expansions.