This paper presents a new approach to singular system analysis by modeling the system in terms of orthogonal triangular functions (TFs). The proposed method is more accurate compared to block pulse function-based analysis with respect to mean integral square error (MISE). A numerical example involving four states of a singular system is treated and solutions obtained thereof. Four tables and relevant curves are presented to compare the respective coefficients in block pulse function (BPF) domain as well as in TF domain. The percentage error of the samples determined via TF domain are compared with the exact samples of the states. Furthermore, MISE for both BPF and TF analysis are computed and compared to reveal the efficiency of TF-based analysis. This paper presents a new approach to singular system analysis by modeling the system in terms of terms of orthogonal triangular functions (TFs). The proposed method is more accurate compared to block pulse function-based analysis with respect to mean integral square error (MISE). A numerical examples involving four states of a singular system is treated and solutions obtained therein. Four tables and relevant curves are presented to compare the respective coefficients in a block pulse function (BPF) domain as well as in TF domain. via TF domain are compared with the exact samples of the states. MISE for both BPF and TF analysis are computed and compared to reveal the efficiency of TF-based analysis.