  The goal of this note is to show that in the case of transversal
intersections the "true local terms" appearing in the Lefschetz trace formula
equal to the "naive local terms". To prove the result we extend the method of
[Va], where the case of contracting correspondences is treated. Our new
ingredients are the observation of Verdier that specialization of any etale
sheaf to the normal cone is monodromic and the assertion that in some cases
local terms are "constant in families". As an application, we get a
generalization of the Deligne-Lusztig trace formula.
