Abstract: The paper derives a variant of classical BOD5 response, matrix used in water quality management planning and attaches numerical examples for illustration. Based upon total load control, a BOD5 input to any river reach appears in the response matrix only once which changes the response from a lower triangular matrix to a sparse matrix in which any single row has three variables. The variant hence increases computational speed. More importantly because the variant has the nice special structure of a transportation problem it can judge conveniently if a water quality management problem is feasible and provides necessary and sufficient conditions of feasibility. This characteristic has significant economic importance in practice. Data demand of the variant and the classical model is the same.