Internet software and service provider J2 Global has extended its $415 million bid to acquire backup storage firm Carbonite.

Carbonite rejected the takeover bid on Jan. 9, according to a Securities and Exchange Commission document. The Boston firm’s Chief Executive Mohamad Ali said in the filing that J2’s offer undervalued the company and was not in the best interest of its stockholders. Carbonite’s board then authorized the company to search for strategic alternatives.

This is the Hollywood company’s second attempt at acquiring Carbonite. J2 is one of Carbonite’s largest shareholders, owning more than 9 percent of its outstanding shares.

The offer, for $15 a share, was set to expire Monday but now has been extended to February 26. Carbonite’s shares closed Tuesday at $14.77, up 7 cents.

J2 Global shares fell 93 cents, or 1.5 percent, on Tuesday to close at $59.50 on the Nasdaq stock market.

Staff reporter Melissah Yang can be reached at [email protected]. Follow her on Twitter @MelissahYang for the latest in L.A. tech news.