  The phase diagram and the order parameters of the exactly solvable quantum 1D
model are analysed. The model in its spin representation is the dimerized XY
spin chain in the presence of uniform and staggered transverse fields. In the
fermionic representation this model is the dimerized non-interacting Kitaev
chain with a modulated chemical potential. The model has a rich phase diagram
which contains phases with local and non-local (string) orders. We have
calculated within the same systematic framework the local order parameters
(spontaneous magnetization) and the non-local string order parameters, along
with the topological winding numbers for all domains of the phase diagram. The
topologically nontrivial phase is shown to have a peculiar oscillating string
order with the wavenumber $q=\pi/2$, awaiting for its experimental
confirmation.
