Contractible edges and bowties in a k-connected graph

Let G be a k-connected graph and let F be the simple graph obtained from G by removing the edge xy and identifying x and y in such a way that the resulting vertex is incident to all those edges (other than xy) which are originally incident to x or y. We say that e is contractible if F is k-connected. A bowtie is the graph consisting of two triangles with exactly one vertex in common. We prove that if a k-connected graph G (k greater than or equal to 4) has no contractible edge, then there exists a bowtie in G.