The paper studies the disturbance decoupling problem by the dynamic measurement feedback for discrete-time nonlinear control systems. To address the problem the algebraic approach, called the algebra of functions, is applied, which allows the system description also depend on non-differentiable functions. A necessary and sufficient condition is given in terms of controlled and (h,f)-invariant functions. Also, algorithms are derived, which find invariant functions and the required feedback. The algorithms are implemented in Mathematica software which is made available over the internet (C) 2013 Elsevier Ltd. All rights reserved.