An apparatus and method for the construction of stairs provides a series of specially-designed brackets to enable the builder to screw or bolt the steps to the inside surface of the stringers, thereby obviating the need to notch the stringers, and avoiding undesirable wood-to-wood contact. In addition, such bolting is considerably more efficient than traditional nailing, and allows easy access to and replacement of the steps and/or hardware when necessary. Furthermore, this bolting and bracket method enables the use of precalculated dimensional instructions for proper location of the brackets on the stringers, and thus is especially conducive to the modular construction and prefabrication of stairs.