Let H be a Hilbert space with {en : n ∈ N} as an orthonormal basis. Let T : H → H be a bounded linear operator defined by Ten = en - 1 + λ sin (2 nr) en + en + 1, where λ is real and r is a rational multiple of π. In this short note it is established that the Moore-Penrose inverse of T is not bounded. We also show that the same conclusion is valid for a few related classes of operators. © 2006 Elsevier Inc. All rights reserved.