ABSTRACT. The notion of an interpolating subspace of a normed linear space was introduced in [1] as a generalization of a Haar subspace in C[a, b]. A very lengthy and nonconstructive proof was given in [1] to show that the real spaces l_{1} and l_{1}^{m} contain interpolating subspaces of every dimension. In this paper we give a constructive proof which is substantially shorter. We also show that quite the opposite is true for the complex spaces l_{1} and l_{1}^{m}. Indeed (Theorem 3.6) no proper subspace M of dimension greater than one is interpolating for any point outside M. (It is clear that the unit vector (1, 0, ...) in l_{1} or l_{1}^{m} spans a one-dimensional interpolating subspace.)