Marriott Corp. will try to accomplish through private transactions what it failed to do with a public offer -- buy back a total of one-third of its outstanding common stock.

Marriott announced yesterday its board of directors had authorized buying up to 3.1 million shares of the company's stock through open market purchases.

The 3.1 million shares is the difference between the number of shares Marriott offered to buy through a public tender offer and the number of shares that stockholders agreed to sell.

Marriott originally offered to buy back 10.6 million shares of its common stock for $23.50 a share. Even after extending the deadline for a week Marriott was about to purchase only 7.48 million shares.

Marriott stock was trading for about $23.50 at the time the tender offer was made but has since fallen back to about $18 a share.

If the company is able to buy the 3 million shares for that price, it could save about $17 million over what the public offering would have cost.

The private purchases could take many months. Marriott earlier repurchased 5 million shares on the open market, but the job took almost a year.

When a company repurchases stock on the open market it is required by securities and Exchange Commission rules to buy the shares in small quantities, so the purchases do not push up the stock's price.

Marriott has said it wants to buy back the stock as part of a restructuring of the company's financial structure. The plan is to reduce the amount of capital raised by stock and replace it with borrowed funds, enabling the company to expand at lower cost.

The stock buy-back would also solidify the control of Marriott family members over the corporation. The Marriotts are not selling their stock back to the company and if the buy-back succeeds they will own enough to absolutely block any take-over attempt.