A novel efficient downstairs trajectory is proposed for a 9 link biped robot model with toe-foot. Brachistochrone is the fastest descent trajectory for a particle moving only under the influence of gravity. In most situations, while climbing downstairs, human hip also follow brachistochrone trajectory for a more responsive motion. Here, an adaptive trajectory planning algorithm is developed so that biped robots of varying link lengths, masses can climb down on varying staircase dimensions. We assume that the center of gravity (COG) of the biped concerned lies on the hip. Zero Moment Point (ZMP) based COG trajectory is considered and its stability is ensured. Cycloidal trajectory is considered for ankle of the swing leg. Parameters of both cycloid and brachistochrone depends on dimensions of staircase steps. Hence this paper can be broadly divided into 4 steps 1) Developing ZMP based brachistochrone trajectory for hip 2) Cycloidal trajectory planning for ankle by taking proper collision constraints 3) Solving Inverse kinematics using unsupervised artificial neural network (ANN) 4) Comparison between the proposed, a circular arc and a virtual slope based hip trajectory. The proposed algorithms have been implemented using MATLAB.