The zeros of a finite-dimensional system can be characterised in terms of the eigenvalues of an operator on the largest closed feedback-invariant subspace. This characterisation is also valid for infinite-dimensional systems, provided that a largest closed feedback-invariant subspace exists. We generalise this characterisation of the zeros to the case when the largest closed feedback-invariant subspace does not exist. We give an example which shows that the choice of domain of the operator on this invariant subspace is crucial to this characterisation.