C. C. Lindner and A. Phelps [“A note on partial parallel classes in Steiner systems”, Discrete Math. 24, 109-112 (1978; Zbl 0401.05020)] proved that for all \(\nu\geq 172\) a Steiner qudruple system of order \(\nu\) has a partial parallel class of cardinality at least (\(\nu\)- 2)/5. In this note the author extends this result to all \(\nu <172\) except possibly \(\nu \in \{20,28,34,38\}\) and here he proves the lower bound (v-7)/5.