  Quantum nonlocality without entanglement is a fantastic phenomenon in quantum
theory. This kind of quantum nonlocality is based on the task of local
discrimination of quantum states. Recently, Bandyopadhyay and Halder [Phys.
Rev. A 104, L050201 (2021)] studied the problem: is there any set of orthogonal
states which can be locally distinguishable, but under some orthogonality
preserving local measurement, each outcome will lead to a locally
indistinguishable set. We say that the set with such property has hidden
nonlocality. Moreover, if such phenomenon can not arise from discarding
subsystems which is termed as local irredundancy, we call it genuine hidden
nonlocality. There, they presented several sets of entangled states with
genuine hidden nonlocality. However, they doubted the existence of a set
without entanglement but with genuine hidden nonlocality. In this paper, we
eliminate this doubt by constructing a series of sets without entanglement but
whose nonlocality can be genuinely activated. We derive a method to tackle with
the local irredundancy problem which is a key tricky for the systems whose
local dimensions are composite numbers. As Bandyopadhyay and Halder have been
pointed out, sets with genuine hidden nonloclity would lead to some
applications on the data hiding.
