A Steiner triple system of order v (STS(v)) is nested if it is possible to add a point to each block and obtain a BIBD(v,4,2). Clearly it is necessary that \(v\equiv 1(mod 6)\). The author points out that, in a sequence of papers, it had been shown that a nested STS(v) is possible whenever \(v\equiv 1(mod 6)\) but with perhaps a few exceptions. Using an unpublished idea of J. Q. Longyear, the author gives a very short and simple proof of the existence of nested STS(v) for all \(v\equiv 1(mod 6)\).