An auxiliary device (1) for a hydraulic brake assembly used on a two-wheel vehicle includes a body (10;10;50) and a transmission device (20;30;40). The body (10;10;50) has two cylinders (11,12;51,52) connected to the left and right brake lever hoses (61,62) comprising movable units (111,121;511,521) driving the transmission device (20;30;40) and two cylinders (13,14;53;54) conneced to the front and rear wheel brake hoses (71,72) comprising two movable units (131,141;531,541) being driven by the transmission device (20;30;40).
By either pulling the left or right brake lever, the front and rear wheel are braked simultaneously via the transmission device (20;30;40).
Preferably, by giving the cylinder (14;54) connected to the rear wheel brake hose (72) a bigger diameter than the cylinder (13,53) connected to the front wheel brake hose (71), the front wheel is braked right after the rear wheel is braked, and the braking force applied to the rear wheel is larger than that to the front wheel.