Let ? = {?1, ?2,...,?n} be a set of complex numbers. The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and sufficient conditions in order that ? may be the spectrum of an entrywise nonnegative n × n matrix. If there exists a nonnegative matrix A with spectrum ? we say that ? is realized by A. If the matrix A must be symmetric we have the symmetric nonnegative inverse eigenvalue problem (SNIEP). This paper presents a simple realizability criterion by symmetric nonnegative matrices. The proof is constructive in the sense that one can explicitly construct symmetric nonnegative matrices realizing ?.