We use a Glauber-like approach to describe very energetic nucleus-nucleus collisions as a sequence of binary nucleon-nucleon collisions. No free parameters are needed: All the information comes from simple parametrizations of nucleon-nucleon collision data. Produced mesons are assumed not to interact with each other or with the original baryons. Comparisons are made to published experimental measurements of baryon rapidity and transverse momentum distributions, negative hadron rapidity and transverse momentum distributions, average multiplicities of pions, kaons, hyperons, and antihyperons, and zero degree energy distributions for sulfur-sulfur collisions at 200 GeV[Formula Presented] per nucleon and for lead-lead collisions at 158 GeV[Formula Presented] per nucleon. Good agreement is found except that the number of strange particles produced, especially antihyperons, is too small compared with experiment. We call this model LEXUS: It is a base-line linear extrapolation of ultrarelativistic nucleon-nucleon scattering to heavy ion collisions.