recently introduced a spectrum for complex solvable Lie algebras of operators, which agrees in the abelian case with the Taylor spectrum for several commuting operators, and proved that their spectrum also satisfies the projection property. This result is correct, but there seems to be a misunderstanding of a theorem of Cartan and Eilenberg in the proof. In this paper we prove the projection property of this generalized Taylor spectrum with the help of the projection property of the approximate point spectrum.