The invention relates to a system for arranging lines in a floor, comprising a primary grid of channels formed in the floor for the purpose of receiving the lines, this primary grid comprising a first and a second series of mutually parallel channels, wherein the channels of the first series and of the second series lie in the same plane and intersect each other perpendicularly. According to the invention the primary grid herein comprises a third series of mutually parallel channels which lie in the same plane as the first and second series of channels and which intersect the channels of the first and second series at non-right angles. The primary grid can optionally comprise a fourth series of mutually parallel channels which lie in the same plane as the first, second and third series of channels and which likewise intersect the channels of the first and second series at non-right angles. A greater flexibility is thus achieved in the choice of the path of the lines in the floor. The invention further relates