  A new object of the probability theory, the two-sided chain of symbols
(introduced in Ref. arXiv:physics/0306170) is used to study isotropy properties
of binary multi-step Markov chains with the long-range correlations.
Established statistical correspondence between the Markov chains and certain
two-sided sequences allows us to prove the isotropy properties of three classes
of the Markov chains. One of them is the important class of weakly correlated
additive Markov chains, which turned out to be equivalent to the additive
two-sided sequences.
