Robotic-assisted needle steering can enhance the accuracy of needle-based interventions. Application of current needle steering techniques are restricted by the limited deflection curvature of needles. Here, a novel steerable needle with improved curvature is developed and used with an online motion planner to steer the needle along curved paths inside tissue. The needle is developed by carving series of small notches on the shaft of a standard needle. The notches decrease the needle flexural stiffness, allowing the needle to follow tightly curved paths with small radius of curvature. In this paper, first, a finite element model of the notched needle deflection in tissue is presented. Next, the model is used to estimate the optimal location for the notches on needle's shaft for achieving a desired curvature. Finally, an ultrasound-guided motion planner for needle steering inside tissue is developed and used to demonstrate the capability of the notched needle in achieving high curvature and maneuvering around obstacles in tissue. We simulated a clinical scenario in brachytherapy, where the target is obstructed by the pubic bone and cannot be reached using regular needles. Experimental results show that the target can be reached using the notched needle with a mean accuracy of 1.2 mm. Thus, the proposed needle enables future research on needle steering toward deeper or more difficult-to-reach targets.