Bourne and Marie drive off to try to find Chernak. Bourne is upset by the news that he might be a cold-blooded assassin. Nonetheless, when Marie tries to escape again and alert the police by shutting off the car's headlights, he cold-bloodedly threatens her life again. (The 2002 movie gets rid of all the kidnapping and threatening and beating up of Marie, making Bourne a lot more likable in the process.)
Marie begs Bourne to let her go, but he tells her he needs her and her driver's license in order to rent a car to get to Paris.
Bourne gets Marie to trick Chernak, who is in a wheelchair, into letting them into the apartment. Marie waits in the bedroom.
The conversation doesn't tell Bourne much he didn't know—and then Chernak pulls a gun and shoots him, shouting about how "Carlos" will pay for his corpse. Bourne is hit, but he manages to throw Chernak out of the wheelchair and shoot him.
Marie is upset by the gunshots and assumes Bourne killed Chernak either out of revenge or to shut him up. When they get to the car, he sort of passes out, and then she escapes.
Marie encounters two men who say that they're police—but one of them has gold-rimmed glasses, which is baaaad news for Marie. She tells them that Bourne killed Chernak. She also tells them where his boarding house is, since he let the information slip.
Bourne heads back to his apartment. St Jacques and the guys who say they're police prepare to go after him.