Unitary group branchings appropriate to the calculation of local invariants of density matrices of composite quantum systems are formulated using the method of S-function plethysms. From this, the generating function for the number of invariants at each degree in the density matrix can be computed. For the case of two two-level systems the generating function is F(q) = 1 + q + 4q^2 + 6 q^3 + 16 q^4 + 23 q^5 + 52 q^6 + 77 q^7 + 150 q^8 + 224 q^9 + 396 q^10 + 583 q^11+ O(q^12). Factorisation of

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... ch series leads in principle to the identification of an integrity basis of algebraically independent invariants. This note replaces Appendix B of our paperus J Phys A33 (2000) 1895-1914 (quant-ph/0001076) which is incorrect.