One of the Bell's assumptions in this original derivation of the inequ
alities was the locality one, i. e. the independence o two separated m
easuring devices. That is why the Bell inequalities breaking, observed
in the experiments, is often interpreted as a demonstration of nonloc
al quantum mechanic features or the contradiction to the local realism
. In this work a straightforward derivation of the Bell inequalities t
raditional form is given, without appealing to locality, but based onl
y on the assumption that the probability distributions is to be nonneg
ative. The same probability distributions are calculated for the concr
ete optical experiment under the quantum theory consideration, and it
is shown that they can be negative. So, the irrelevance of the Bell in
equalities breaking to the locality assumption is strictly proved. The
physical nature of the obtained results is examined.