In recent years, damage detection, as determined by variations in the dynamic characteristics or response of structures, has received considerable attention in the literature. This paper proposes a new damage identification technique that identifies damage location. A methodology termed the Two-Points Condensation Technique (TPC) is presented. It uses identification of stiffness matrix terms to assess damage, based on the incomplete measurement of captured vibration test data. This study identifies damage using free vibration test data in the time domain. Most other techniques used at present are based on data in the frequency domain. The TPC method uses a set of matrices by reducing the structural system to a two-degrees-of-freedom system and then compares the identified coefficients of the stiffness matrices with the coefficients of the theoretically condensed stiffness matrices. The damage location is obtained by observing the change in value of the stiffness coefficients of the two-degrees-of-freedom systems. For the computation, an optimisation uses a program written in MATLAB code. The code can be executed both under the MATLAB and Octave environments. The TPC technique is applied to experimental data obtained from a steel beam model structure after introducing a thickness change in one element. Two case studies are considered. In both cases, the method accurately detects the damage, and determines its location. In addition, the results illustrate that observing changes in the stiffness matrix coefficients can be a useful tool for monitoring structural health. As the procedure proposed here is in a time domain, to eliminate time-consuming calculations this procedure is suitable for structures that are not continuously monitored, but are monitored within scheduled time periods.