CORRECTED-(OFFICIAL)-U.S. private sector added 158,000 jobs in Oct-ADP

(Corrects to show September was revised again to gain of 114,000)

NEW YORK, Nov 1 (Reuters) - U.S. companies added 158,000 jobs in October, data from a payrolls processor showed on Thursday in a revamped report on the private sector labor market.

The ADP National Employment Report showed September's job gains were revised up to 114,000 after initially being revised to 88,200 as part of ADP's new methodology. Under the old method, September's gain was originally reported as 162,000.

Economists had forecast October's report would show a gain of 135,000 jobs, according to a Reuters poll.

Economists often refer to the ADP report to fine-tune their expectations for the nonfarm payrolls report due on Friday, though it is not always accurate in predicting the outcome. The overhaul is meant to bring ADP's numbers more in line with the government's final revised jobs figures.

(Reporting by Leah Schnurr; Editing by Chizu Nomiyama)