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Employing new infrared radial velocities, we have computed spectroscopic orbits of the cool giants in four southern S-type symbiotic systems. The orbits for two of the systems, Hen 3-461 and Hen 3-828, have been determined for the first time, while orbits of the other two, SY Mus and AR Pav, have previously been determined. For the latter two systems, we compare our results with those in the literature. The low mass of the secondary of SY Mus suggests that it has gone through a common envelope phase. Hen 3-461 has an orbital period of 2271 days, one of the longest currently known for S-type symbiotic systems. That period is very different from the orbital period proposed previously from its photometric variations. The other three binaries have periods between 600 and 700 day, values that are typical for S-type symbiotic orbits. Basic properties of the M giant components and the distance to each system are determined.