Presented is a new measuring and reconstruction framework of Compressed Sensing (CS), aiming at reducing the measurements required to ensure faithful reconstruction. A sparse vector is segmented into sparser vectors. These new ones are then randomly sensed. For recovery, we reconstruct these vectors individually and assemble them to obtain the original signal. We show that the proposed scheme, referred to as SegOMP, yields higher probability of exact recovery in theory. It is finished with much smaller number of measurements to achieve a same reconstruction quality when compared to the canonical greedy algorithms. Extensive experiments verify the validity of the SegOMP and demonstrate its potentials.