The behavior of a multiplicity independent root-finding scheme in the presence of error

King and Kioustelidis independently proposed a derivative free scheme that permits root finding methods, such as the secant method to preserve high order convergence when the root in question is multiple. In this note it is shown that the scheme can fail to achieve the maximum accuracy that is attainable at a fixed precision of computation.This work was supported in part by the Office of Naval Research under contract No. N00014-76-C-0391.