Undefined reference error when I try to call compiled NASM function from C program

I have a c program, to optimize this program I have tried this:

1. compile the most heavy method (named my_method) separately
2. disassembly the compiled method
3. editing the assembly code generated from the compiler to optimize this
4. compile edited and optimized assembly code with NASM compiler

the original c method has this signature

float **my_method(int m, int n, float **MatrixA, float **VectorB){
   //method boby
}

The problem: How to call the compiled optimized "NASMed" version of the method from C?

I have tried to declare this at the beginning of the c file

extern float **my_method(int m, int n, float **MatrixA, float **VectorB);

but when I try to call the method in c for example with

float **res= mymethod(rows, columns, matrix1, vect);

GCC returns me this error: Undefined reference to my_method

the compiled assembly file is named my_method.o my c file is named my_program.c

I have tried to compile with gcc my_program.c