Skype sure is cool. If only it actually did something to help eBay (Nasdaq: EBAY) sell more stuff in its signature auctions.

Don't expect that to happen soon. On Monday, the Web phone wonder put out a press release that makes mention of eBay only once. Here: "Skype is an eBay company ..."

I guess we're done pretending that there's (ahem) synergy here.

At least the news is cool. Skype is introducing a $9.95-per-month global plan that will allow users to call out to any mobile or landline phone in 34 countries. The move expands upon earlier plans that allow similar calls to select European Union countries or all 50 U.S. states. Activity charges? They don't apply unless you use more than 10,000 minutes per month.

Innovations like this are what make Skype appealing to me and 309 million other users of its service. But will any of it help eBay?

Some will say it'll become easier for eBayers to do business cross-continent. I disagree. Skype-to-Skype calls have always been free. Were this really the sales-enabler that former CEO Meg Whitman pitched it to be, a $1.4 billion impairment charge wouldn't have been necessary.

Here's some advice, eBay. Now that Skype does not seem to recognize your importance to its business, it's time for you to do the same. Sell, get what you can, and get back to the business you were born for. The one that still, after all these years, has Amazon (Nasdaq: AMZN) and Overstock.com (Nasdaq: OSTK) green with envy.

Auctions.

Going once ... Going twice ... Sold!

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Fool contributor Tim Beyers didn't own shares in any of the companies mentioned in this article at the time of publication. You can find Tim's portfolio and his latest blog entry. The Fool's disclosure policy was sick last night and couldn't come up with something witty. (Sniff.)