This paper proposes the use of the square root of the sum of squares (SRSS) spatial combination rule in combination with a newly defined critical response spectrum, SACRIT, to arrive at improved estimates of the maximum values of the various response quantities of an irregular building with no principal axes, The SACRIT represents the maximum amplitudes on the orbit plots of a bi-directional oscillator with different natural periods excited simultaneously by two horizontal components of ground motion, similar to the pendulum in a structural response recorder (SRR). Application of this response spectrum along any two arbitrarily selected orthogonal axes of a single story irregular building has been shown to provide the maximum response amplitudes in very good agreement with the exact time history solution for several sets of real accelerograms with widely differing amplitude and frequency characteristics. The application of the proposed method is illustrated for a very simple building just for the purpose of brevity to minimize the influence of the mode superposition method used to estimate the partial contribution to the response due to each component of motion. On theoretical grounds, the proposed method is expected to be equally applicable to more complex multi-degree-of-freedom buildings also, which will be illustrated in a future paper.