  We compute the next-to-leading, O(m alpha^5), contribution to the hyperfine
splitting in positronium within the framework of NRQED. When applied to the
ground state, our calculation reproduces known results, providing a further
test of NRQED techniques. Besides providing a very simple method of calculation
of the standard result, we also obtain new expressions for excited states of
positronium with negligible additional effort. Our calculation requires the
complete next-to-leading matching of the lowest-dimension NRQED four-fermi
couplings, which we publish here for the first time.
