The Klein quadric Q⁺(5, q) in the five-dimensional projective space PG(5, q) is a fundamental object in projective geometry, representing the set of lines in the three-dimensional projective space PG(3, q). In PG(3, q), where q is even, the set of all secant lines to a hyperbolic quadric forms a well structured and geometrically significant family. These secant lines, which intersect the hyperbolic quadric Q⁺(3, q) in two points, correspond under the Klein correspondence to a specific subset of Q⁺(5, q) in PG(5, q). Here, we introduce a new characterization that identifies when a set of lines in PG(3, q) can be recognized as the set of secant lines to Q⁺(3, q), using properties of  properties of Q⁺(5, q).