We perform first-principles Formula Presented plus Bethe-Salpeter equation calculations to investigate the photophysics of monolayer hexagonal boron nitride (Formula Presented), revealing excitons with novel Formula Presented-space characteristics. The excitonic states forming the first and third peaks in its absorption spectrum are Formula Presented-like, but those of the second peak are notably Formula Presented-like, a first finding of strong co-occurrence of bright Formula Presented-like and bright Formula Presented-like states in an intrinsic 2D material. Moreover, even though the Formula Presented-space wave function of these excitonic states are centered at the Formula Presented and Formula Presented valleys as in monolayer transition metal dichalcogenides, the Formula Presented-space envelope functions of the basis excitons at one valley have significant extents to the basin of the other valley. As a consequence, the optical response of monolayer Formula Presented exhibits a lack of circular dichroism, as well as a coupling that induces an intervalley mixing between Formula Presented- and Formula Presented-like states.