The Turan Number of F3,3

Let F-3,F-3 be the 3-graph on 6 vertices, labelled abcxyz, and 10 edges, one of which is abc, and the other 9 of which are all triples that contain 1 vertex from abc and 2 vertices from xyz. We show that for all n >= 6, the maximum number of edges in an F-3,F-3-free 3-graph on n vertices is ((n)(3)) - (([n/2])(3)) - (([n/2])(3)). This sharpens results of Zhou [9] and of the second author and Rodl [7].