We know that if we set $K$, $F$ and $L$ fields, with $L$ a finite extension of $F$ and $F$ a finite extension of $K$. Then we have the norm equality $$N\_{L/K}=N\_{F/K}\circ N\_{L/F}$$ The common proof is by using rational canonical forms and elementary matrices. I was wondering if there is a way only by using the tools of field extensions. Thank you.