What bird did kill one of the wood pidgins?

Some days ago I hurried into the garden to get lettuce for dinner. I wasn’t that far from the bird in the pictures below when I noticed it. It looked at me, but was busy plucking another bird and didn’t fly away despite my approach in a hurrying gait. I walked slowly backwards and watched it from inside the house.

Then I thought I might get a picture, as it was so concentrated on its activity. So I went out with the camera, which has a very wide angle, that’s why zooming didn’t bring the bird very near.

Anyway, I managed to get as near to it as before, and did take the first picture before it flew away to where I took the second. I thought he was plucking a blackbird, but it turned out that the victim was a wood pidgin, which is somewhat larger in size than the bird itself I’d say.

Anyway, I guess it was a sparrowhawk, but I didn’t find the rectangular feature on its head that I see on my pictures on any drawings or pictures of these birds that I could find.

Here’s what was left of the poor wood pidgin:

If anyone can help determine what predatory bird that is I’ll be thankful.