The space

of bivariate generalised Hermite polynomials of degree n is invariant under rotations. We exploit this symmetry to construct an orthonormal basis for

which consists of the rotations of a single polynomial through the angles

, ℓ=0,...n. Thus we obtain an orthogonal expansion which retains as much of the symmetry of

as is possible. Indeed we show that a continuous version of this orthogonal expansion exists.