P.Ara and K.R.Goodearl, in , introduced and studied the concept of a regular ring R satisfying the following condition, which they called condition (D): ϕ(k0(r)+) is dense in Aff(S(Ko(R),[R]))+, where ϕ denotes the natural map from Ko(R) to Aff(S(Ko(R), [R])).They proved that every nonartinian, stably finite, strictly unperforated, simple regular ring satisfies condition (D). In this note we prove that a regular ring R satisfies condition (D) if and only if R has no nonzero artinian homomorphic image. We then obtain as a consequence that every nonartinian, simple regular ring satisfies condition (D). © 1994, Taylor & Francis Group, LLC. All rights reserved.