This note corrects an error in a paper recently published in this journal (An optimal algorithm to compute all the covers of a string, Inform. Process. Lett. 50 (5) (1994) 239-246). The correction consists primarily of a new subalgorithm which is called by COMPUTE_COVERS, the main algorithm presented in the paper referenced. It turns out that the new subalgorithm it itself sufficient to solve the original problem - that is, to compute all the covers of a given string in time linear in the string length - and so it is presented here as a self-contained algorithm in its own right.