I feel weird to write about an adapter that has no name, because if you want to buy one, I can't tell you want brand it is. But this one looks very different than most other EXA to EOS adapters. Do a search on eBay and you should find one. Mine cost $18USD with free shipping from Hong Kong.
I had two Exakta to EOS adapters which I bought few years ago, and both of them could not make the lenses focus to infinity, despite what the seller claimed. I decided to give it another try when I saw an ultra-thin adapter, which arrived very promptly from Hong Kong few days ago after I bought it from eBay. Few of of my Exakta mount lenses have shutter button arm on the lens and the arm prevents the lens from mounting flat on the adapter. Some lenses with longer arms, like the Topcor 10cm f2.8 and the 5.8cm f1.8, can not be mounted on the Canon DSLRs at all. What a pity. For those with shorter arms, like the Pancolar 50mm f2 and the Flegtogon 35mm f2.8, I had to file the raised portion on the arm to mount the lens on the adapter; see picture #3.
It turns out that the new adapter can in fact focus the lenses to infinity, but at a cost. It's very thin and mounts more towards the mirror box than other EXA-EOS adapters, and on the 5D Mark II, it catches the mirror and you can't use it with the optical view finder. I must un-mount the lens/adapter, turn on live-view, flip up the mirror and then mount the lens/adapter. When the mirror is disengaged, it will just rest on the rear of the adapter and that should be OK. Whenever I need to take pictures, I will need to flip the mirror up and use it like a mirrorless camera without a viewfinder.
The new adapter mounts VERY tightly to the lens. Because it's so thin, you can't mount it without using a rag or towel to cushion the edge, so that it won't cut you as you apply force. Unlike most adapters, the locking mechanism is not spring loaded. This means you have to keep an eye on the locking pin as you mount the lens and when the locking pin on the lens is at the center of the notch on the locking mechanism of the adapter, you have to push it down to lock it; see picture #4 below. To un-mount the lens, you would have to manually flip up the locking mechanism to unlock, and then un-mount the lens.
Here is the good news if you don't use a 5D/5D II. This adapter works with my 20D (1.6x), and 1D Mark III (1.3x). The mirror on these two cameras did not hit the lens/adapter even at infinity focus. I would assume all crop-sensor Canon are OK, and possibly the 1Ds series of full frame bodies are also fine. So, perhaps, only the 5D/5D II (don't know about the 5D III) have problems. Also, the adapter is quite precise. If you set the lens to infinity, it's in focus. This means you don't have to check focus if you are going take pictures far away; just set the lens to infinity and you know it will be in focus.
New adapter on left, old adapter on right. Notice the old (silver) one is larger, which is not good as it will interfere more with the arm on the lens.
Thickness test - new one is 0.68mm, old one is 1.04mm. Anything thicker than 0.7mm will not attain infinity focus.
The raised portion on the arm has to be filed flat in order for the adapter to mount flush.
Mounted - Note the manual locking/unlocking mechanism.