In this paper, we study the input-output decoupling and linearization of nonlinear two-input two-output time-varying delay systems. When working with delay systems, two problems may arise when constructing a feedback transformation for which the input-output map of the feedback modified systems is linear. The first issue is the boundedness of the control and the second one is its causality. We develop an algorithm allowing the construction of a causal and bounded feedback which permits to solve the input-output decoupling and linearization problem. The idea of our algorithm is to introduce, at each step, when the input-output decoupling is not possible, an artificial delay for the input that appears " too early " in the system. To that end, we propose, at each step, a precise procedure for defining a simple feedback transformation.