A flock of a cone in PG(5,q) with a line as vertex and a hyperbolic quadric Q +(3, q) as base is associated with every locally hermitian 1-system of Q +(7, q) and conversely, so that the two objects are equivalent. We construct an example of such a flock, starting from a Segre variety S 1;2 , and study the corresponding 1-system of Q +(7, q). Locally hermitian semiclassical 1-systems of Q +(7, q), which are not contained in a hyperplane of PG(7,q) , are characterized in terms of their flock. Finally, the previously known locally hermitian semiclassical 1-systems of Q +(7, q) are investigated and it seems that many new examples can be found.