  Recently the construction of the non-abelian effective D-brane action was
performed through order $\alpha'{}^3$ including the terms quadratic in the
gauginos. This result can be tested by calculating the spectrum in the presence
of constant magnetic background fields and comparing it to the string theoretic
predictions. This test was already performed for the purely bosonic terms. In
this note we extend the test to the fermionic terms. We obtain perfect
agreement.
