Second time is a charm?

CBC Canada: Corel returns as publicly traded company. Corel’s stock price closed at $17.95, down 16 cents from the company’s initial public offering price of $18.11.
Shares in Corel, which was taken private in 2003 by San Francisco-based Vector Capital, also began trading on Nasdaq after being priced at $16 US. The stock finished at $15.85 US.

If a public company is taken private, then sells shares to the public again, does this still count as an IPO? After all, this isn’t exactly its “initial” public offering. I’ve added updated the Corel contracts page with the contracts from their most-recent IPO.