A t-regular self-complementary k-hypergraph, denoted by $$\hbox {SRHG}(t,k,v)$$ , is a k-hypergraph with a v-set V as vertex set and an edge set E, such that every t-subset of V lies in the same number of edges and there is a permutation $$\sigma \in S_v $$ with the property that $$e\in E$$ if and only if $$\sigma (e)\notin E$$ . It is clear that a set of trivial necessary conditions for the existence of an $$\hbox {SRHG}(t,k,v)$$ is that $${v-i\atopwithdelims ()k-i}$$ is an even integer for all $$i=0,1,...,t$$ . In this paper, we extend the method of partitionable sets for constructing large sets of t-designs to obtain new $$\hbox {SRHG}(t,k,v)$$ . In particular, we present $$\hbox {SRHG}(2,3,10)$$ , $$\hbox {SRHG}(2,4,10)$$ , $$\hbox {SRHG}(2,4,11)$$ and $$\hbox {SRHG}(2,5,10)$$ . Also we show that the trivial necessary conditions for the existence of $$\hbox {SRHG}(2,k,v)$$ with $$k\le 7$$ are sufficient.