Like Scott and Sage have both pointed out, the Federal Reserve is audited every year. In fact, those audits are required by law and that law can be found at 12 USC Chapter 3 http://uscode.house.gov/view.xhtml?path=/prelim@title12/chapter3&edition=prelim Scroll down to section 248b. These are complete financial audits and are not restricted in any way.
In addition to those audits, the GAO is authorized by law to perform many reviews of Federal Resevre operations and does so every year as well. See 31 USC Section 714 http://uscode.house.gov/view.xhtml?hl=false&edition=prelim&req=granuleid%3AUSC-prelim-title31-subtitle1&num=0&saved=L3ByZWxpbUB0aXRsZTMxL3N1YnRpdGxlMy9jaGFwdGVyMzk%3D%7CZ3JhbnVsZWlkOlVTQy1wcmVsaW0tdGl0bGUzMS1jaGFwdGVyMzk%3D%7C%7C%7C0%7Cfalse%7Cprelim Scroll down to section 714. Also, the FOUR restrictions on GAO audits are listed in 714b. Those restrictions were put there by Congress, not the Federal Reserve.
BTW, the results of all of these audits and reviews ARE PUBLIC RECORD and are available on the Internet for anyone who bothers to look for them. Therefore, your claim about them having something to hide is obviously false since you could look at them any time you wanted if you only took the few seconds to look for them.
Ron Paul and his followers won't accept the reality that the Federal Reserve is audited every year because they are either 1) too stupid to look at the audit reports, or 2) have an irrational hatred of the Federal Reserve, or 3) both. BTW, most reasonable thinking people that actually have a clue about economics would tell you that getting rid of the Federal Reserve and putting monetary policy directly into the hands of the politicians would be a really bad idea.
Link to the audited financial statements of the Federal Reserve: http://www.federalreserve.gov/monetarypolicy/bst_fedfinancials.htm
Link to GAO reports on the Federal Reserve: http://www.gao.gov/browse/a-z/Federal_Reserve_System,_Independent_Agencies
Finally, anyone who gives this answer a 'thumbs-down' is only showing that they are delusional. I have provided links to the law requiring the audits. I have provided links to the audit results. The audit results are public record and are provided not only on the Federal Reserve and GAO websites but are also presented to Congress in the Federal Reserve annual reports. That is irrefutable evidence that the Federal Reserve IS audited every year and claims to the contrary are nothing but conspiracy theory nonsense.