  We analyse the splitting of exact flat bands in the chiral model of the
twisted bilayer graphene (TBG) when the $AA'/BB'$ coupling of the full
Bistritzer--MacDonald model is taken into account. The first-order perturbation
caused by the $AA'/BB'$ potential the same for both bands and satisfies
interesting symmetries, in particular it vanishes on the line defined by the
$K$ points. The splitting of the flat bands is governed by the quadratic term
which vanishes at the $K$ points.
