Constraints Across Normalized Tables

Dear Experts,

When I use a single table I can easily use constraints to enforce my
business logic, but what do I do when I normalize a single table into
multiple tables.

For example, imagine that my initial table has the columns ID, Name,
Salary with the constraint that Salary is not NULL. Now imagine that
I break this into two tables, one with ID and Name and another with ID
and Salary. I would like to have a constraint that prevents the
creation of a row with (ID,Name) in the first table unless a
corresponding row in the second table is also created.

I can enforce this logic with triggers, but it looks ugly and is
fairly brittle. Is there a better way or is this the dark side of
normalization?

Thanks.