The synthesis of biochemical pathways satisfying stoichiometric constraints is discussed. Stoichiometric constraints arise primarily from designating compounds as required or allowed reactants, and required or allowed products of the pathways; they also arise from similar restrictions on intermediate metabolites and bioreactions participating in the pathways. An algorithm for the complete and correct solution of the problem is presented; the algorithm satisfies each constraint by recursively transforming a base-set of pathways. The algorithm is applied to the problem of lysine synthesis from glucose and ammonia. In addition to the established synthesis routes, the algorithm constructs several alternative pathways that bypass key enzymes, such as malate dehydrogenase and pyruvate dehydrogenase. Apart from the construction of pathways with desired characteristics, the systematic synthesis of pathways can also uncover fundamental constraints in a particular problem, by demonstrating that no pathways exist to meet certain sets of specifications. In the case of lysine, the algorithm shows that oxaloacetate is a necessary intermediate in all pathways leading to lysine from glucose, and that the yield of lysine over glucose cannot exceed 67% in the absence of enzymatic recovery of carbon dioxide.