Accountants first devised GAAP as a set of rules for accreditation in the accounting field. Colleges and universities in the U.S. have adopted the same concept as a standard for accreditation. The problem is that there are no standard rules associated with GAAP. Different agencies use the term "generally accepted" to mean different things. Also, an agency can call itself an accrediting agency with no recognition from any other agency. This is a shortcoming in this system of accreditation and will not be solved without central governmental oversight of the whole process.
An accrediting agency in the U.S. is deemed acceptable under GAAP if it has recognitions from either the Council on Higher Education Accreditation or the U.S. Department of Education. Note that there is no law that prohibits an agency from calling itself an accreditation agency even if it is not recognized by one of these two organizations. Therefore there are a large number of unrecognized agencies that may give questionable accreditation to an institution. Note that being unrecognized does not necessarily mean that the agency is bad or has ill-intentions. It may be that its founders do not agree with GAAP principles or the procedures for the above two organizations. However, it is very difficult to determine whether the agency is doing good accreditation if it is not a recognized agency.
The accreditation procedure is very vague, specially due to non-standardization of the associated rules and principles. Each agency develops and follows its own procedures. For example, one agency may make it mandatory to send educational specialists to the institution for a thorough review of the institutions teaching methods, research and facilities. Another agency may decide not to do that. One agency may give higher weight to research while another may give teaching higher preference.
The database of institutions accredited by recognized U.S. accrediting organizations can be found in the references. It should be noted that there also are a number of accrediting agencies that are not recognized by either Council on Higher Education Accreditation or the U.S. Department of Education. Their accreditation standards may be questionable and it is advisable to ask the school about the accrediting agency as well. If an institution calls itself accredited, all that means is that some agency, recognized or unrecognized, has given its seal of approval. Whether that agency is trustworthy is another thing. Therefore the best strategy is to insist on knowing whether the accrediting agency is a recognized one.