Necessary and sufficient conditions for positive realness in terms of state-space matrices are presented under the assumption of complete controllability and complete observability of square systems with independent inputs. By a particular transform of these conditions, a direct algorithm for testing positive realness is determined that requires only checking a set of simple algebraic conditions. This provides an alternative procedure to the positive real lemma and to the s-domain inequalities. Based on this algorithm, a synthesis of a positive real system via output feedback is presented.