Let N($d_1,...,{;}d_n;c_1,...,{;}c_n$) be the number of solutions $(x_1,...,{;}x_n){in}F^{n}_p$ of the diagonal equation $c_lx_1^{d_1}+c_2x_2^{d_2}+{cdots}+c_nx_n^{d_n}{;}={;}0{;}n{geq},{;}c_j{;}{in}{;}F^{*}_q,{;}j=1,2,...,{;}n$ where $d_j{;}>{;}1{;}and{;}d_j{;}$mid${;}q{;}-{;}1$</TEX> for all j = 1,2,..., n. In this paper, we find all n-tuples ($d_1,...,{;}d_n$) such that the reduced form of ($d_1,...,{;}d_n$) and N($d_1,...,{;}d_n;c_1,...,{;}c_n$) are the same as in the theorem obtained by Sun Qi [3]. Improving this, we also get an explicit formula for the number of solutions of the diagonal equation, unver a certain natural restriction on the exponents.