A new meta-GGA exchange functional based on an improved constraint-based GGA

► New meta-GGA that comes from an improved constrained-based GGA. ► The conversion of the GGA to meta-GGA is based on the procedure for revTPSS. ► The proposed meta-GGA satisfies the large reduced density gradient constraint. ► The meta-GGA leads to a rather good description of heats of formation. ► The meta-GGA leads to a rather poor description of reaction barrier heights.