What is the title of the black/white film about a couple on a killing spree?

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New member
Some years ago I saw this movie but am unable to find it anywhere.

It is about a US army truck driver who falls in love with a girl in the town he is stationed in (during some war).
They later accidentally kill someone and as more people find out they kill them and try to hide all these murders.
It ends with both of them being shot in front of some big building.

That is all I remember but I hope it is enough information for someone who has seen it to identify the film.
 
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