Tsao and Wright (1983) proposes the use of a metric called the “maximum ratio” to (deterministically) test whether one of K competing estimates of an unknown population parameter θ is outside of an “acceptable” region, whose radius is a multiple α × θ for some α ∈ (0, 1). Hall (2024) generalizes this (deterministic) test to a (deterministic) “multidimensional maximum ratio” test that assesses whether some vector composed of elements from K G-dimensional estimates of an unknown G-dimensional population parameter θ is outside of an “acceptable” region, whose radius is a multiple α × ∥θ∥ for some α ∈ (0, 1). This test flags collections of elements taken from these estimates as unacceptable, rather than flagging individual G-dimensional estimates. As a result, it can give false positives when there are unacceptable collections of elements but all estimates are acceptable. This paper proposes a (deterministic) maximum ratio test for G-dimensional parameter estimates that will not give false positives, proves its validity, and compares its performance to the multidimensional maximum ratio test discussed by Hall (2024).