  A set of multipartite orthogonal product states is locally irreducible, if it
is not possible to eliminate one or more states from the set by
orthogonality-preserving local measurements. An effective way to prove that a
set is locally irreducible is to show that only trivial
orthogonality-preserving measurement can be performed to this set. In general,
it is difficult to show such a orthogonality-preserving measurement must be
trivial. In this work, we develop two basic techniques to deal with this
problem. Using these techniques, we successfully construct orthogonal product
sets (OPSs) in any possible three, four and five-partite systems that are
locally irreducible in every bipartition. Moreover, we also show the existence
of unextendible product bases (UPBs) with such properties in $d\otimes d\otimes
d$ for any $d\geq 3$. Therefore, these OPSs and UPBs exhibit the phenomenon of
strong quantum nonlocality without entanglement. Both results solve the open
questions given by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)] and Yuan
et al. [Phys. Rev. A 102, 042228 (2020)]. Our results shed a new light on the
strong quantum nonlocality without entanglement.
