Raising timber floor level.

hello folks,

I am raising the floor level 4 " on a 1940 house. I will be using 4" joists on the original concrete floor. One room however already has a joist timber floor. This was an extension done in the 60 s. When I raised the floor boards, the joists next to the external wall have some rot.
Anyway, in order to raise this floor, is it ok to lay joist across the original joists?

Thanks in advance.

Eamon