The nation's money supply fell $400 million in the week ended Oct. 31 in addition to a $600 million downward revision in the previous week's figures, the Federal Reserve announced yesterday.

M-1, the measure of money that includes currency in circulation and checking account deposits in commercial banks, dropped to $376.5 billion in the latest week. That is substantially below the level for the week ended Oct. 3, which after other revisions now stands at $379.7 billion.

For the latest four weeks, M-1 averaged $378.2 billion. That means M-1 has grown at only a 6.3 percent annual rate from the comparable figure 13 weeks previously, a rate within the Fed's target range for M-1.

The slowdown in the rate of growth of the money supply now evident is a sharp change from the apparent situation prior to the Federal Reserve's decision Oct. 6 to tighten credit conditions substantially. However, most money market experts say the slowdown has come too soon to be attributable to those actions.

The fed also announced it has hired the Washington law firm of Fulbright & Jaworski to investigate whether any individuals or institutions obtained improper advantage from preparation, revision or release of the money supply figures in recent weeks.

Money supply figures will appear in tomorrow's edition.