A Twitter page is displayed on a laptop computer in Los Angeles, Oct. 13, 2009. (Mario Anzuoni/Reuters)

Twitter announced Tuesday that it is updating the way it handles security for its social network, introducing a new security option that it promises is both more secure and easier-to-use than its current two-factor authentication system.

Until now, if you wanted more security on your account than just a username and password, you could ask Twitter to send you a text message every time you wanted to sign in to the Web client. From Tuesday, the company’s rolling out a new system that dispenses with the text message altogether. All users need now is their phone and a Twitter app to sign in to the service.

Twitter has a pretty great gif of how the system works on its blog post on the more technical aspects of the system, but essentially users will see in-app alerts asking them to approve or reject Web log-in requests. And because the social network will also give you information on when and where you — or others — have tried to access your account, you should get a better handle on when someone is trying to crack into your account.

Twitter first added two-factor authentication in May, following a rash of high-profile attacks on accounts including that of the Associated Press. Pranksters used that account to spread a fake report of an explosion at the White House.

But the system it used, which relied on text messages, didn’t work with all devices — the iPod Touch, for instance — making it a less-than optimal solution. Even with the new security enabled, users should remain wary of messages from people they don’t know, particularly if those messages contain links. Basically, you should always follow the first rule of Web security: When in doubt, delete, delete, delete.