Alibaba Group's latest message to Yahoo sounds a lot like the last one: it wants its shares back.

CEO Jack Ma took full control of one of China's largest online payment businesses, Alipay, from the Alibaba Group, Yahoo said in a government filing on Tuesday. The U.S. online search engine's shares fell as much as 9.8 percent on Wednesday as a result.

The move hurts Yahoo because it owns 43 percent of Alibaba -- considered one of its most valuable assets. Now that asset has one less hot property on its hands.

Investors valuing Yahoo on its sum of the parts will have to remove Alipay from the equation, Stifel Nicolaus analyst Jordan Rohan wrote in a research note.

Oppenheimer Equity Research estimated that Alipay represents

about $1.7 billion of Yahoo's market value of about $24 billion.

Yahoo's Asian assets, which include a 35 percent stake in Yahoo Japan, are considered prized possessions by some investors since they represent at least half of Yahoo's market value and an increasing growth opportunity, according to some estimates.

Investor David Einhorn's hedge fund Greenlight Capital took a significant position in Yahoo last week, citing the Internet company's valuable Asian assets and estimating Yahoo's stake in Alibaba was ultimately worth Yahoo's entire current market value.

While Yahoo is one of the world's most popular Web destinations, it is struggling to keep its foothold as people flock to Google and social media networks like Facebook.

The Alipay restructuring sets the stage for possible talks between Alibaba Group, which owns China's largest e-commerce company, and Yahoo over reducing Yahoo's stake in the company.

The two companies have been at odds for some time over Yahoo's stake.

It's not a secret that Jack Ma has been trying to negotiate a way to reduce Yahoo's stake, said Eric Jackson, managing member of Ironfire Capital which holds shares in Yahoo. I would anticipate a lot of feverish discussions in the background between these parties.

Jackson described the Alipay restructuring as a bargaining chip in negotiations.

Alibaba, Yahoo and Softbank Corp, also a principal stakeholder, are in discussions about the terms of the Alipay restructuring, said a Yahoo spokeswoman.

Alipay is required to get a license from the People's Bank of China to operate its payment business and this move might speed that process, she added.

Yahoo Chief Executive Carol Bartz told Reuters in September that Alibaba constantly approaches Yahoo about repurchasing its stake, but Yahoo has no plans to sell it.

Yahoo invested $1 billion in the Alibaba Group in 2005.

I would be comfortable if Yahoo sold 10 percent back, Jackson said. Theoretically Yahoo could hold out and play a game of chicken. Then things like today happen.

(Reporting by Jennifer Saba. Editing by Robert MacMillan)