  Form factors of the weak $\Xi_c \to \Xi(\Lambda)$ transitions are calculated
within the light cone QCD sum rules. The pollutions coming from the
contribution of the negative parity $\Xi_c^*$ baryon is eliminated by
considering the combinations of sum rules corresponding to the different
Lorentz structures. Having obtained the form factors, the branching ratios of
the $\Xi_c \to \Xi (\Lambda) \ell \nu$ decays are also calculated, and our
predictions are compared with the results of other approaches as well as the
measurements done by BELLE and ALICE Collaborations.
