  We propose an extended Bogoliubov transformation in real space for spinless
fermions, based on which a class of Kitaev chains of length $2N$ with zero
chemical potential can be mapped to two independent Kitaev chains of length
$N$. It provides an alternative way to investigate a complicated system from
the result of relatively simple systems. We demonstrate the implications of
this decomposition by a Su-Schrieffer-Heeger (SSH) Kitaev model, which supports
rich quantum phases. The features of the system, including the groundstate
topology and nonequilibrium dynamics, can be revealed directly from that of
sub-Kitaev chains. Based on this connection, two types of
Bardeen-Cooper-Schrieffer (BCS)-pair order parameters are introduced to
characterize the phase diagram, showing the ingredient of two different BCS
pairing modes. Analytical analysis and numerical simulations show that the
real-space decomposition for the ground state still holds true approximately in
presence of finite chemical potential in the gapful regions.
