rank of unitary matrices

Question

Let $U:=[u_1,\cdots,u_n] \in \mathbb{C}^{n,n}$ with $u_i \in \mathbb{C}^n$ for $i=1,\cdots,n$ be a unitary matrix. Why is $u_j u_j^H$ a rank one matrix for $j=1,\cdots,n$?

($u_j^H$ denotes the conjugate transpose)