  Context. Many disk galaxies host two extended stellar components that rotate
in opposite directions. The analysis of the stellar populations of the
counter-rotating components provides constraints on the environmental and
internal processes that drive their formation.
  Aims. The S0 NGC 1366 in the Fornax cluster is known to host a stellar
component that is kinematically decoupled from the main body of the galaxy.
Here we successfully separated the two counter-rotating stellar components to
independently measure the kinematics and properties of their stellar
populations.
  Methods. We performed a spectroscopic decomposition of the spectrum obtained
along the galaxy major axis and separated the relative contribution of the two
counter-rotating stellar components and of the ionized-gas component. We
measured the line-strength indices of the two counter-rotating stellar
components and modeled each of them with single stellar population models that
account for the {\alpha}/Fe overabundance.
  Results. We found that the counter-rotating stellar component is younger, has
nearly the same metallicity, and is less {\alpha}/Fe enhanced than the
corotating component. Unlike most of the counter-rotating galaxies, the ionized
gas detected in NGC 1366 is neither associated with the counter-rotating
stellar component nor with the main galaxy body. On the contrary, it has a
disordered distribution and a disturbed kinematics with multiple velocity
components observed along the minor axis of the galaxy.
  Conclusions. The different properties of the counter-rotating stellar
components and the kinematic peculiarities of the ionized gas suggest that NGC
1366 is at an intermediate stage of the acquisition process, building the
counter-rotating components with some gas clouds still falling onto the galaxy.
