We present a new family of exchange biased Single Molecule Magnets in which antiferromagnetic coupling between the two components results in quantum behaviour different from that of the individual SMMs. Our experimental observations and theoretical analysis suggest a means of tuning the quantum tunnelling of magnetization in SMMs. See also: W. Wernsdorfer, N. Aliaga-Alcalde, D. Hendrickson, G. Christou, Nature 416 (2002) 406.