a lot of them DO work with the S4 still that are "older" mhl adapters, but you also need the 5 to 11 pin adapter for those to work like this: http://www.amazon.com/gp/aw/d/B0089V...110_SY165_QL70
Otherwise, just get one line what was noted a couple of posts up, as it's already utilizing the 11pins and saves you the trouble. (make sure you're getting a legit one & check the reviews!)
Alternately, you can get the allshare cast hub (by Samsung) which also mirrors via hdmi.
It is also possible without an mhl dongle or allshare cast hub to push things (pics, movies & youtube) directly if you have tv/home theater/blu ray that's dlna enabled to push to.
I've done it from the older mhl w/ 11 pin adapter, newer 11 pin, allshare hub & by dlna enabled device without issue. I mainly use the latter nowawdays, but still use the other methods on occasion because of the screen mirroring.
As a side note, both mhl adapters are OEM.