Former Fed Chairman Alan Greenspan said on Sunday that signs of stabilization and increased confidence in the economy could be dashed if home prices were to take another turn downward.

Greenspan told ABC's This Week With George Stephanopoulos that he didn't believe that a steep drop was in store, but home prices had stabilized only temporarily.

It is possible that could get a second wave down, Greenspan said. Under those conditions, we would get a very significant change in the underlying confidence in the consumer area, as foreclosures rise and more home values fall below their mortgage levels.

(Reporting by David Lawder)