It seems like Google is finally complying with the Recording Industry Association of America's wishes by not showing alleged copyright infringing Web sites in its Instant and Autocomplete search features.

According to TorrentFreak, the search giant just added the Pirate Bay to its censorship list.

Now, when users type "thepiratebay.org" or any of the site's other domain names into their search box, nothing relating to the Pirate Bay's Web site pops up. However, the file-sharing site is still indexed in Google's overall search function.

The RIAA has been working hard over the past couple of years urging Google and other search engines to block any results that could lead users to sites with illegally obtained copyrighted material. The association believes this type of censorship could help cut down on online piracy.

The Pirate Bay is one of those sites singled out by the RIAA, but the file-sharing site has said its traffic wouldn't change a bit if search engines censor it.

"Right now about 10 percent of our traffic comes from these competing search engines. With that ban in place that means that our traffic numbers probably will increase," the Pirate Bay wrote in a blog post in June. "Users will go directly to us instead and use our search instead. We'll grow even more massive."

According to TorrentFreak, Google began filtering out "piracy-related" terms in its Instant and Autocomplete searches in January 2011. So when users search "BitTorrent," "uTorrent," "MegaUpload," and "Rapidshare," these words don't come up unless they are entirely typed out.

On Google's Autocomplete help page, it says, "While we always strive to algorithmically reflect the diversity of content on the web (some good, some objectionable), we also apply a narrow set of removal policies for pornography, violence, hate speech, and terms that are frequently used to find content that infringes copyrights."

It seems that Google believes the Pirate Bay must be infringing on copyrights. Despite Google taking these measures and removing sites from its search feature, a French court redundantly ruled in July that the search giant had to delete "torrent" from Autocomplete.

In addition to censoring certain Autocomplete searches, Google also complies with requests to remove URLs that allegedly host copyrighted or pirated material. In a May report, the search giant said it receives an average of 1.2 million such requests per month and complies with 97 percent of them.

CNET contacted Google for more information on why it removed the Pirate Bay from its Autocomplete feature. We'll update the story when we hear back.