Carl Icahn has yet another idea for PayPal.

In a statement published today, the activist investor pitched the idea that parent company eBay conduct an IPO of PayPal in which 20 percent of the electronic payments service is sold to the public.

In his proposal, eBay would keep the remaining 80 percent. A long-term contract between the companies would preserve “all synergies,” he said, adding:

“This type of relationship is customary in partial IPOs and would be particularly important for eBay as currently, outside of PayPal, there does not exist a global payment processing solution competent enough to service eBay’s users.”

The point? Icahn said this arrangement would “provide the best opportunity for these businesses to remain competitive over the long-term,” while what he describes as “the secret sauce” of PayPal’s techniques and technologies at eBay would be maintained in the majority portion:

“A 20 percent IPO of PayPal could allow for all of the benefits of an independent PayPal, preserves all of the benefits of keeping PayPal in-house and could be structured so as to be tax-free to shareholders.”

Icahn has been on a major campaign to pry PayPal from eBay, and his letter makes clear that a key driver is the possibility of a higher valuation for shareholders of a separated PayPal.

He also suggests in today’s letter that the publicly traded PayPal stock could work for acquisition and in recruiting top talent. In addition, Icahn said a partially independent PayPal could pursue more partnerships, such as with the credit card companies or with Facebook, and it would develop a “startup mentality” that leads to expanded product offerings.

In response, eBay management issued a statement late Wednesday afternoon that said in part:

“PayPal and eBay are better together. That’s been true for the past five years, during which time PayPal and eBay have generated a 441 percent increase in share price for our investors. …

“PayPal has not been held back by eBay Inc. In fact, as part of eBay Inc., PayPal has built relationships with Visa, MasterCard, American Express, and Discover, with the world’s leading point-of-sale providers, and with leading global companies such as Facebook and Samsung. …

“A partial separation of PayPal is not a new idea, and we’re glad to see that Mr. Icahn now seems to agree that a full separation of PayPal is not a good idea… In the future, our board will continue to evaluate all strategic options and make the right decisions for shareholders. But today, PayPal and eBay are better together.”

Outside of Icahn, some others have suggested that PayPal could become the world’s largest bank — if only it wasn’t under eBay.

But not all eBay-watchers agree.

“It sounds like [a PayPal spinoff] would be doing things that would be competitive [with eBay],” James Wester, the research director for global payments at industry research firm IDC, told VentureBeat. “PayPal works well because it has that base of eBay users, and it gains volume and stability from having these eBay transactions over the eBay network.”

The spun-off portion of PayPal, Wester noted, would be focused more on quarter-to-quarter results because of the need to satisfy shareholders, but now “a lot of their ability [to do things] is because they’re part of eBay” and don’t have that short-sightedness.

“One of the problems with the payments business,” he added, “is it seems like they should be valued more, but there are very, very, very small margins on awesome volumes.”