Is it possible for a signal handler to survive after "exec"?

I wrote a signal handler for a process, and fork() after that, the signal handler will be applied to both parent and child processes. If I replace the child process with "exec", the signal handler is no more.

I know this happens because "exec" call will overwrite the child process address space with it's own. I just want to know if there is a way to make signal handler work even after "exec" call ?