Federal auditors have found that Matthew N. Novick, ousted last week as inspector general of the Environmental Protection Agency, had a secretary do personal typing for him on government time, but they generally cleared him of other allegations.

A former secretary to Novick spent about 10 1/2 hours typing a term paper and a job application for Novick's son, a resume for a friend of Novick and personal letters to Novick's credit card companies, according to a draft report by the General Accounting Office. A copy of the report was obtained by The Washington Post.

The secretary "stated that Mr. Novick directed her to do this work on government time," the report said. Novick told the auditors he thought the typing was being done after working hours.

The White House did not cite the GAO investigation or any other reason for ousting Novick last week, and administration officials have indicated that he will be given another job.

Novick was dismissed days after the release of a critical inspector general's audit of the EPA's toxic waste cleanup fund. Rep. James H. Scheuer (D-N.Y.) has charged that President Reagan fired Novick in an attempt "to limit the bad news."

The GAO report, which will be sent to EPA Administrator Anne M. Burford, found no evidence to support allegations that Novick used his government driver for personal errands and that he improperly helped a woman he was dating obtain at job at the EPA.