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Abstract: The norm principle for a division algebra states that the image of the reduced norm is an invariant of its Brauer-equivalence class. This can be generalized to symbols in $K^M_1(F)$ the Milnor K-group. We prove a generalized norm principle for symbols in $K^M_n(F)$ for a prime-to-$p$ closed field $F$ of characteristic zero (for some prime $p$).  We also give a new proof for the norm principle of division algebra, by decomposition theorem for (noncommutative) polynomials over the algebra.