Script to remove image orientation

I need to remove the orientation "flag" of a batch of images (jpeg images), without changing the displayed orientation of the images.

Trying to make it clear : if I have an image in portrait orientation with an orientation flag, I want it to keep this portrait orientation, but get rid of the orientation flag, as it seems some application are not able to handle it correctly. It's a kind of fusionning the image with its orientation flag.

I guess this means recompressing the image, but that is not a problem.

I tried to do it with automator, but was not able to do it. Is it possible ?