Summary: We consider the \textsf{Unconstrained Submodular Maximization} problem in which we are given a nonnegative submodular function \(f:2^{\mathcal{N}}\to \mathbb R^+\), and the objective is to find a subset \(S\subseteq \mathcal{N}\) maximizing \(f(S)\). This is one of the most basic submodular optimization problems, having a wide range of applications. Some well-known problems captured by \textsf{Unconstrained Submodular Maximization} include \textsf{Max-Cut}, \textsf{Max-DiCut}, and variants of \textsf{Max-SAT} and maximum facility location. We present a simple randomized linear time algorithm achieving a tight approximation guarantee of 1/2, thus matching the known hardness result of \textit{U. Feige} et al. [SIAM J. Comput. 40, No. 4, 1133--1153 (2011; Zbl 1230.90198)]. Our algorithm is based on an adaptation of the greedy approach which exploits certain symmetry properties of the problem.