(Daniel Acker/Bloomberg via Getty Images)

After vocal backlash on Tuesday against Facebook's policy on violent images, the company took down a video of a woman's beheading from the website.

The social networking site had enforced a temporary ban on graphic videos in May, but then quietly lifted the ban during the summer, arguing that as long as users were uploading the content in order to condemn violence rather than glorify it, it was fair game.

But Facebook did an about-face - sort of - on Tuesday around 6 p.m.

"We took down the video. We're trying to strengthen how we enforce the policies we already have on graphic videos," Facebook spokesman Matt Steinfeld told ABC News today. "It's not a reversal on our policy; we'll still allow graphic violence on the site if it's condemning. We're just going to look at a broader set of factors: where does the video come from, how is it being shared, does the user have warnings that it's graphic content, etc."

In its official statement, Facebook said that "as part of our effort to combat the glorification of violence on Facebook, we are strengthening the enforcement of our policies."

The company said they will review based on the holistic context and whether the user is sharing it responsibly by accompanying it with a warning.

"Based on these enhanced standards, we have re-examined recent reports of graphic content and have concluded that this content improperly and irresponsibly glorifies violence," the company stated. "For this reason, we have removed it."

The video purportedly shows a woman being beheaded in Mexico.

Earlier Tuesday, Facebook allowed the video to remain on the site since the company believed the content was shared for an educational purpose and not in a sadistic manner.

"It's a good thing they took it down. Those videos are absolutely horrific," said Mark Potok, senior fellow at the Southern Poverty Law Center. "I've seen them myself - they are psychologically damaging. Good for them for finally coming around to the obviously right decision."