UPDATE 2-Twitter says looking for independent director to replace Elliott's Cohn

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April 1 (Reuters) - Twitter Inc said on Thursday it was looking for an independent board director after hedge fund Elliott Management's managing partner, Jesse Cohn, decided to relinquish his board seat at the social media firm.

Twitter said it will consult with Cohn before finalizing a candidate. Cohn, who is being nominated for a re-election to the board at the 2021 annual meeting of stockholders, will resign once a new director is appointed, the company added.

Last year in March, Twitter reached an agreement with Elliott to add three new directors for letting Jack Dorsey stay as chief executive officer, days after Elliott's plan to push out the company's chief became public.

Twitter added Cohn, and private equity firm Silver Lake's co-chief executive officer Egon Durban to its board and said it planned to appoint a third new director soon.

Dorsey is one of Silicon Valley's most prominent entrepreneurs who also runs Square Inc, a mobile payments company he co-founded. (Reporting by Akanksha Rana in Bengaluru and Greg Roumeliotis; Editing by Shinjini Ganguli)