Hackers have now flooded the Internet with virus-tainted e-mails that target anyone using the social-networking site.
Anti-virus software company MacAfee says thousands of Facebook users have been receiving an e-mail which tells them that the password on their Facebook account has been reset.
The users are then urged to click on an attachment to get new log-in credentials.
If the attachment is opened, it downloads malicious software, including a program that steals passwords.
Facebook is advising users not to even open the e-mail and to just delete it and warn their friends.
