  Hidden variables are well known sources of disturbance when recovering belief
networks from data based only on measurable variables. Hence models assuming
existence of hidden variables are under development.
  This paper presents a new algorithm "accelerating" the known CI algorithm of
Spirtes, Glymour and Scheines {Spirtes:93}. We prove that this algorithm does
not produces (conditional) independencies not present in the data if
statistical independence test is reliable.
  This result is to be considered as non-trivial since e.g. the same claim
fails to be true for FCI algorithm, another "accelerator" of CI, developed in
{Spirtes:93}.
