In this paper strict negative-imaginariness is defined in input-output sense, which is different from the notion of existing strictly negative-imaginary systems. The class of output strictly negative-imaginary systems is characterized in state-space with respect to a non-negative parameter δ. The newly defined class of output strictly negative-imaginary systems forms an intersection with the existing class of strictly negative-imaginary systems. Further, a time-domain definition is also provided to classify strict and non-strict negative-imaginary systems in dissipative framework which is applicable to both linear and nonlinear cases. Several numerical examples are given to show the usefulness of the key results.