This brief addresses the problem of vision-based robot control where the equilibrium state is defined via a goal image. Specifically, we consider the class of intensity-based nonmetric solutions, which provide for high accuracy, versatility, and robustness. Existing techniques within that class present a fully coupled translational and rotational control error dynamics, what increases analysis complexity and may degrade system performance. This paper proposes a new intensity-based nonmetric visual servoing technique that decouples the translational control error dynamics, regardless of the observed object characteristics, camera displacements, and their relative poses. The obtained system is thus lower-triangular in the general case. For some practical cases, the proposed general technique leads to the Grail of a fully decoupled (i.e., strictly diagonal) linear dynamics. Theoretical analysis of local diffeomorphism, local exponential stability, and of those decoupling properties are provided. Improved performances are also experimentally confirmed using a six-degree-of-freedom robotic manipulator in various positioning and tracking tasks.