General :: Program Includes .so Which Includes .a?

I have prepared a static lib(.a) comprising 2 function definitions. I have created a different shared library(.so) comprising 2 more functions. The two functions of .so use the functions defined in the .a file. That is, the .so file uses the services of the .a file. Next, I create an executable that uses the shared library(.so). When I build my executable, it needs to be linked with the .a file as well. it gives me undefined reference for the functions defined in the .a file. Why is that so? I am posing this question because, the .a file has already been included(static linking) while bulding the .so. Is there any workaround so that I need not link the .a file with my final executable?