  We show that the long-time limit of the two-point correlation function
obtained via the standard quantum regression theorem, a standard tool to
compute correlation functions in open quantum systems, does not respect the
Kubo-Martin-Schwinger equilibrium condition to the non-zero order of the
system-bath coupling. We then follow the recently developed Heisenberg operator
method for open quantum systems and by applying a ``{\it weak}" Markov
approximation, derive a new modified version of the quantum regression theorem
that not only respects the KMS condition but further predicts exact answers for
certain paradigmatic models in specific limits. We also show that in cases
where the modified quantum regression theorem does not match with exact
answers, it always performs better than the standard quantum regression
theorem.
