We consider an N-particle system of noncolliding Brownian motion starting from x (1)a parts per thousand currency signx (2)a parts per thousand currency signaEuro broken vertical bar a parts per thousand currency signx (N) with drift coefficients nu (j) , 1a parts per thousand currency signja parts per thousand currency signN satisfying nu (1)a parts per thousand currency sign nu (2)a parts per thousand currency signaEuro broken vertical bar a parts per thousand currency sign nu (N) . When all of the initial points are degenerated to be zero, x (j) =0, 1a parts per thousand currency signja parts per thousand currency signN, the equivalence is proved between a dilatation with factor 1/t of this drifted process and the noncolliding Brownian motion starting from nu (1)a parts per thousand currency sign nu (2)a parts per thousand currency signaEuro broken vertical bar a parts per thousand currency sign nu (N) without drift observed at reciprocal time 1/t, for arbitrary t > 0. Using this reciprocal time relation, we study the determinantal property of the noncolliding Brownian motion with drift having finite and infinite numbers of particles.