It's common knowledge that Yahoo! (NASDAQ:YHOO) and Microsoft (NASDAQ:MSFT) have been talking about some sort of combination again. Last year's thwarted merger discussions couldn't keep Microsoft away forever.

Most observers focus on Microsoft trying to again buy Yahoo!, or at least on buying Yahoo!'s search operations. All of these ideas are supposed to close the gap between search leader Google (NASDAQ:GOOG) and the Microsoft laggards. But that's all backwards.

Yahoo! should buy Microsoft's online operations.

What Redmond should be doing is ...
Yeah, you read that right: Microsoft should just give up the whole Google chase and refocus on doing the things Microsoft is really good at. Operating systems, enterprise-class software, other software tools for consumers, and even a few lines of excellent hardware spring to mind. That's what Microsoft should be doing to the exclusion of nearly everything else.

And throwing billions of dollars and untold man-hours after a vainglorious attempt to become a market leader in online search, advertising, or content portals is just misguided.

Mr. Softy's squandered advantages
Microsoft owns the operating system on nearly every computer at your office or in your home. Apple (NASDAQ:AAPL) is the closest competitor with a puny 9.8% market share, according to data from Net Applications. Internet Explorer is the default Web browser in the 88% of all computers that run Windows. And in IE, the default search engine is Live or Bing, depending on how often you update your search providers. You can change the default search engine and browser, but it's an extra step that many people don't bother with.

Despite all of these material advantages, Microsoft still can't get a handle on the Internet search market. Google owns 64% of all U.S. search traffic, according to market tracker ComScore, and is taking market share from all other major players even now.

Turn the beat around
So, Microsoft wants to buy its way into prosperity in a field it clearly doesn't know how to dominate, even when given a head start and handcuffing the competition. Meanwhile, the online division is losing money and dragging down the rest of the world's largest software company.

Better then, say I, to cut the apron strings and hand off this failing operation to someone who knows how to run a successful online operation. Yahoo! would be the first choice, given its knack for making a profit and churning out positive cash flows -- from the sort of business model Microsoft is trying to emulate. With $3.3 billion of liquid assets on hand and no long-term debt weighing down its credit rating, Yahoo could surely afford to acquire Microsoft's substantial user base and give them something better than the confusing MSN/Live/Bing platform.

One buyout to rule them all
There really isn't even a second choice for me. Proven online successes like Amazon.com (NASDAQ:AMZN) and eBay (NASDAQ:EBAY) have tried and failed at search operations before, and wouldn't bring much to the table. IAC/InterActive (NASDAQ:IACI) has the fourth-largest search engine in Ask.com, but can't match Yahoo!'s money-making prowess and rock-solid financial stability. Some complete dark horse could emerge from the shadows, but I don't see the point in muddling the already murky waters even further. Only Yahoo! truly makes sense as a suitor.

MSN should be folded into Yahoo!, fully digested, and then forgotten. Millions of Hotmail users could easily use the Yahoo! Mail interface to handle their communications, and let's be serious -- would you miss Bing if it was gone or engineered into Yahoo!'s search offerings?

Yeah, I didn't think so.

The end result of a reverse Yahoo! deal
The result would be a leaner, meaner Microsoft with a tighter focus on its own true core strengths. In Sunnyvale, Yahoo! would gain a large (but not overwhelming by any means) influx of fresh users, a few well-entrenched Web addresses like msn.com, live.com, and Hotmail; and a batch of Microsoft-trained engineers who could shake things up with fresh ideas. New CEO Carol Bartz seems keen on poking at the status quo in a company that stagnated under Terry Semel.

Both companies would arguably be better off, and a reinvigorated Yahoo! could really challenge Google at the top. A Microsoft Online division with all of Yahoo!'s assets thrown in stand less of a chance at reaching that pinnacle. Give it up, Redmond. Get back to doing what you do best and defend your core operating system and enterprise strengths against new technologies that threaten your dominant position. There's still plenty of growth in these areas, and a more focused management structure could do wonders. Throw this process in reverse.

More Foolishness about the Microsoft-Yahoo! wobbly waltz:

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Fool contributor Anders Bylund owns shares in Google, but he holds no other position in any of the companies discussed here. He believes that if the other guys could get their act together, they'd drive Google to work harder for its shareholders. You can check out Anders' holdings or a concise bio if you like, and The Motley Fool is investors writing for investors.