(Refiles to fix headline to "bounce back", not "bounce bank")

LONDON, Nov 4 (Reuters) - European shares bounced back on Wednesday after steep losses in the previous session, with financials and miners gaining ground ahead of the U.S. Federal Reserve's rate decision and statement on the economy.

At 0806 GMT, the FTSEurofirst 300 index of top European shares was up 0.7 percent at 975.90 points after falling 1.2 percent to a one-month closing low on Tuesday. The index, which is up 17 percent so far in 2009, has gained 51 percent since hitting a record low in early March.

"The macro data flow has been very positive over the last couple of days and I think the markets can go a bit higher from here," said Klaus Wiener, head of research at Generali Investments.

Banks rebounded, after steep losses on Tuesday following disappointing results from UBS (UBSN.VX: Quote, Profile, Research) and sharp declines in Royal Bank of England (RBS.L: Quote, Profile, Research) shares. The DJ STOXX European banking index gained 1.3 percent.

UBS was up 2 percent, while Royal Bank of Scotland rose 3.8 percent. Standard Chartered (STAN.L: Quote, Profile, Research), HSBC (HSBA.L: Quote, Profile, Research), Barclays (BARC.L: Quote, Profile, Research), Lloyds (LLOY.L: Quote, Profile, Research) and BNP Paribas (BNPP.PA: Quote, Profile, Research) gained 1 to 2.7 percent.

Societe Generale (SOGN.PA: Quote, Profile, Research) was up 3.3 percent. It doubled its third-quarter net profit from a year ago, but said the economic environment remained uncertain. [ID:nL3620732]

Miners got strength from higher metals prices. BHP Billiton (BLT.L: Quote, Profile, Research), Anglo American (AAL.L: Quote, Profile, Research), Antofagasta (ANTO.L: Quote, Profile, Research), Rio Tinto (RIO.L: Quote, Profile, Research), Xstrata (XTA.L: Quote, Profile, Research) and Eurasian Natural Resources (ENRC.L: Quote, Profile, Research) rose 1.1 to 2.7 percent.

The Fed is expected to reaffirm at the end of its two-day meeting on Wednesday that policies to support the economy will stay in place for some time, even as signs of recovery mount. [ID:nFEDAHEAD] (Reporting by Atul Prakash)