"I'm using Keil, but I think my issue is more a C langage issue."

Yes, I think so

*** file1.h ***.

xdata variable[]={0x01, 0x02, ....}; //128 values

You haven't specified the type of this variable - therefore 'C' will assume int

You shouldn't put the variable definition in a header (.h) file; only declarations should go in headers!

I've covered this before - do a 'Seach' for "declaration" AND "definition"

"even if I change the 'variable' values, the compiler always uses old values for which I don't know how it has kept it!"

Not quite sure what you mean by this?

Do you really mean that you have a compile-time problem, or is it a run-time problem?
Or both??

At run-time, it's probably because of the definition in your header - this mean that each file contains a separate definition of 'variable' - so changes to one would not affect the other!

Presumably, you actually wanted just one definition, with the other file making an external reference?

void Display (U8 *variable)

You defined 'variable' as an int (presumably by accident) - so this is not going to give correct results!