  The $\it{\Xi_{cc}^{++}\to \Xi_{c}^{'+}\pi^{+}}$ decay is observed using
proton-proton collisions collected by the LHCb experiment at a centre-of-mass
energy of $13\mathrm{\,Te\kern -0.1em V}$, corresponding to an integrated
luminosity of $5.4\,\mathrm{fb}^{-1}$. The $\it{\Xi_{cc}^{++}\to
\Xi_{c}^{'+}\pi^{+}}$ decay is reconstructed partially, where the photon from
the $\it{\Xi_{c}^{'+} \to \Xi_{c}^{+}\gamma}$ decay is not reconstructed and
the $pK^-\pi^+$ final state of the $\it{\Xi_{c}^{+}}$ baryon is employed. The
$\it{\Xi_{cc}^{++}\to \Xi_{c}^{'+}\pi^{+}}$ branching fraction relative to that
of the $\it{\Xi_{cc}^{++}\to \Xi_{c}^{+}\pi^{+}}$ decay is measured to be $1.41
\pm 0.17 \pm 0.10$, where the first uncertainty is statistical and the second
systematic.
