Clunie and Sheil-Small [‘Harmonic univalent functions’, Ann. Acad. Sci. Fenn. Ser. A. I. Math.9 (1984), 3–25] gave a simple and useful univalence criterion for harmonic functions, usually called the shear construction. However, the application of this theorem is limited to planar harmonic mappings that are convex in the horizontal direction. In this paper, a natural generalisation of the shear construction is given. More precisely, our results are obtained under the hypothesis that the image of a harmonic function is a union of two sets that are convex in the horizontal direction.
