* To sell 20 pct of Covisint in IPO, distribute rest to shareholders
* Initiates annual dividend of 50 cents per share
* Elliott says Compuware agrees for due diligence
* Compuware shares rise 6.5 percent
Jan 25 (Reuters) - Business software maker Compuware Corp said on Friday it was open to a better offer after turning down a $2.3 billion bid from Elliott Management Corp, and the hedge fund said it remained "very interested".
Compuware shares rose 6.5 percent to $11.46, above Elliott's December offer of $11 per share, in heavy trading on the Nasdaq.
Compuware said on Friday Elliott's offer was just too low and chose instead to proceed with spinning off a non-core unit, responding to criticism that the company was underperforming.
The company also said it would pay its first-ever annual dividend, of 50 cents per share, and would cut costs.
"The board will carefully review and evaluate any credible offer it receives, including from Elliott, that delivers full value to it shareholders," Compuware Chief Executive Bob Paul said on a conference call.
"We have spoken to Elliott throughout this process and will maintain an open door for dialogue with them."
A spokesman for Elliott, Compuware's third-largest shareholder, said the company had agreed to its request to undertake due diligence.
"We will immediately reach out to negotiate an appropriate NDA (non-disclosure agreement) and look forward to moving quickly to engage in diligence with the help of our legal and financial advisers," Jesse Cohn, a portfolio manager at Elliott Management, said in an emailed statement.
"We remain very interested in the company," Cohn said.
Elliott declared an 8 percent economic interest in Compuware when it made its offer on Dec. 17. In a Jan. 24 filing, Elliott said it beneficially owned 14.2 million shares, or 6.6 percent of the outstanding shares.
Compuware said on Friday it expected to sell a 20 percent interest in its Covisint cloud software business in an IPO and distribute the rest among its shareholders.
The company filed for a possible IPO of its Covisint cloud software business last year. It has not disclosed how much it plans to raise.