Construction of caps by means of caps in complementary subspaces

A construction of caps is given which yields in particular caps with a free pair of points. Applying this construction, we meet the bound of Farr and Lisoněk [J. Farr, P. Lisoněk, Caps with free pairs of points, J. Geom. 85 (2006) 35–41] for caps with a free pair of points in PG(5,q), qq even.