If U and V are bands (idempotent semigroups), are there circumstances under which their free product U*~ V, in the variety ~ of bands, belongs to a proper subvariety ~/" of ~? There are some positive results in a few special cases. It is well known that if U and V are both trivial, then U*~ V is normal. Jones [3] showed that if U and V are both semilattices, then U*~ V is regular. It is an easy exercise, as we will demonstrate shortly, to show that if U and V are rectangular bands, U*~ V satisfies a band identity defining a proper subvariety. However, we will present an example where u is a normal band, V is trivial, and U*~ V does not satisfy any band identity defining a proper subvariety. This obviously puts an upper bound on results of the aforementioned nature. However, as something of a converse, we are able to show that if U is right normal (dually left normal) and V is a rectangular band, then U*~ V lies in a proper subvariety of bands. The example discussed and the methods of proof used in this paper have been suggested from the examples and ideas displayed in Olin [6]. Throughout this paper, U and V will be assumed to be normal bands, i.e. those satisfying the identity axya = ayxa, in addition to the basic band identity x 2 =x. Bands are discussed in Petrich [7, Chapter II] and in Howie [2, Chapter IV]. The main structure theorem for bands states that "every band is a semilattice of rectangular bands" [2, Theorem IV. 3.1]. In the case of normal bands, this can be strengthened to "every normal band is a strong semilattice of rectangular bands" [2, Theorem IV. 5.14]. This means that if U is a normal band, it has the following properties: (i) U = l..Jo~A Do~, where A is a semilattice and each D~ is a rectangular band; and, (ii) if re, fle A, tr -> fl, then there exists a homomorphism ~o~,a:Do,---~Da, where (a) if tr=fl, then ~o~.~ is the identity mapping; (b) tr, fl, yeA, o:>-fl>-7, then ~o~,7 = q~,~o q~,~; and (c) ifa ~D~ and b ~D~, then ab = (ad?~,~)(bdp~,~t~). Let 6e be the variety of semigroups, and let w be an element of U*~e V. Then w is a word gl �9 " "gn where, for 1 <- i <- n - 1, gi ~ U(V) implies &§ e V(U), and