Open Question: Movie assistance please! I remember an old 1950s movie about a man & women trying to kill eachother.?

Its an old black & white movie from the 1950s (I guess). I remember the ending: Each says good-bye & drives off in their own car in different directions. They both feel guilty & turn around & race to eachother & confess theres bombs in each cars! I think they embrace & the movie ends. Its not Mr & Mrs Smith (2005) or the 1941 movie with the same name.