Sallie Mae, the giant education-finance company, said yesterday that it is offering to buy back $4.3 billion of its Student Loan Marketing Association subsidiary's debt, which will complete the process of turning the company into a completely private enterprise.

The offer, which company officials said is designed to take advantage of favorable market conditions, will complete the privatization early next year, a year ahead of the current schedule and three years before the deadline set by Congress when it initiated the process in 1996.

The Student Loan Marketing Association was founded as a government-sponsored enterprise -- a congressionally chartered, shareholder-owned company -- to buy government-guaranteed student loans from private lenders to make more loans available to students. Congress in the late 1990s directed that it become fully private.

New management, led by chief executive Albert L. Lord, took over in a proxy fight in 1997, promising greater growth and profits through increased diversification of the company's offerings.

The company, renamed SLM Corp. but keeping the nickname Sallie Mae, has grown significantly and now offers a variety of services, including loans and collections.

Sallie Mae has been shifting assets out of the subsidiary, a process that was 98 percent complete on June 30, executives said. The buyback offer is meant to remove the last of its debt, $7.9 billion at the end of June. Much of that debt will mature by early next year and the company is offering to buy back the remaining longer-term securities, which total $4.3 billion.