In this article, we give a new characterization of positive absolutely minimum attaining operators in terms of essential spectrum. We discuss absolutely minimum attaining property of multiplication operator on a σ-finite measure space and then establish a spectral decomposition for normal absolutely minimum attaining operators. We also give a sufficient condition under which the adjoint of an absolutely minimum attaining operator is absolutely minimum attaining and show that a paranormal absolutely minimum attaining operator with an extra condition is hyponormal. In the end, we prove a few spectral properties of paranormal operators. © 2019, Tusi Mathematical Research Group (TMRG).