In the present work, the fission of the solitary capillary gravity waves at the threshold is treated using the Korteweg-de Vries equation with the variable coefficients. It turns out that the convex/concave solitary wave can disintegrate into one, i.e. H. the transformation of the convex solitary wave into the concave wave and vice versa is not possible at the threshold. While convex solitary wave fission occurs only with decreasing liquid depth, concave solitary wave fission can occur with both decreasing and increasing liquid depth.