This study investigates a parameterization of all output-rectifying retrofit controllers for distributed design of a structured controller. It has been discovered that all retrofit controllers can be characterized as a constrained Youla parameterization, which is difficult to solve analytically. For synthesis, a tractable and insightful class of retrofit controllers, referred to as output-rectifying retrofit controllers, has been introduced. An unconstrained parameterization of all output-rectifying retrofit controllers can be derived under a technical assumption on measurability of the interaction signal. The aim of this note is to reveal the structure of all output-rectifying retrofit controllers in the general output-feedback case without interaction measurement. It is found out that the existing developments can be generalized based on system inversion. The result leads to the conclusion that output-rectifying retrofit controllers can readily be designed even in the general case.