The enzyme acts on inositol 1,4-bisphosphate and inositol 1,3,4-trisphosphate (forming inositol 3,4-bisphosphate) with similar Vmax values for both substrates, but with a five-times higher affinity for the bisphosphate. Does not act on inositol 1-phosphate, inositol 1,4,5-trisphosphate or inositol 1,3,4,5-tetrakisphosphate.