One of Yahoo's largest shareholders has urged company leaders to sell its search business to Microsoft.

Ivory Investment Management, which has 21.4 million, or 1.5% of Yahoo's shares, sent a letter Wednesday to Yahoo's board of directors urging them to move quickly to shore up a deal with Microsoft. As time passes, both companies allow Google to expand its advantage in the search market, Ivory said.

"This deal would offer Microsoft the unique opportunity to immediately gain critical mass to better level the playing field with Google, while it would simultaneously allow Yahoo to both receive a sizable upfront cash payment and increase its prospective cash flow," Ivory said in the letter.

Ivory proposed allowing Microsoft to own and operate a combined search platform, while Yahoo would be an affiliate and collect 80% of the revenue from search ads on its own site. It also stated that Microsoft should become the search engine for Yahoo's current search affiliates.

Ivory said that such a deal could give Yahoo shareholders $24 to $39 per share. That's double or more of Yahoo shares' current value.

"Yahoo could receive more than $15 billion upfront from Microsoft for its search business and increase EBITDA by more than $500 million per annum," the shareholder said in the letter.

Ivory said Yahoo and Microsoft likely spend more than $1 billion annually on search, while combining and streamlining operating costs could save $800 million and help increase total search revenue by 20%, or $500 million or more, annually.

"Even accounting for a reasonable margin of error in our estimates and assumptions, there is no question the proposed deal would significantly increase shareholder value," the firm wrote, adding that the benefit could soar to a 140% increase from current trading.

Ivory urged Yahoo to maximize shareholder value and expressed concern over its failure to do so when it turned down an offer of $31 per share earlier this year. That's well above Yahoo's opening of $12.69 per share Wednesday.