Let T be an operator on a Banach space X that is similar to − T via an involution U. Then,U decomposes the Banach space X as X = X 1 ⊕ X 2 with respect to which decomposition we have U = ( I 1 0 0 − I 2 ) , where I i is the identity operator on the closed subspace X i (i = 1, 2). Furthermore, T has necessarily the form T = ( 0 ∗ ∗ 0 ) with respect to the same decomposition. In this note, we consider the question when T is a commutator of the idempotent P = ( I 1 0 0 0 ) and some idempotent Q on X. We also determine which scalar multiples of unilateral shifts on l p spaces ( 1 ≤ p < ∞ ) are commutators of idempotent operators.