For a ring R, let ip（RR）={a ∈ R： every right R-homomorphism f from any right ideal of R into R with Imf = aR can extend to R}. It is known that R is right IP-injective if and only if R = ip（RR） and R is right simple-injective if and only if {a ∈ R ： aR is simple} ∪→ ip（RR）. In this note, we introduce the concept of right S-IP-injective rings, i.e., the ring R with S ∪→ ip（RR）, where S is a subset of R. Some properties of this kind of rings are obtained.
