To improve the utilization rate of construction waste, reduce processing costs, and improve processing efficiency, we used near-infrared hyperspectral technology to extract and classify typical construction waste types. We proposed the pythagorean wavelet transform (PWT) to get the characteristic reflectivity to avoid the redundancy of hyperspectral data. Compared with the results from the wavelet transform (WT), we were able to retain more detailed information, and we observed the enhancement of differences between different species. To adapt to the complex conditions present in actual situations and to improve our ability to distinguish similar spectrum, we extracted, in addition to the characteristic reflectivity, four potential features. After classified verification, we found out that the first derivative and the intrinsic mode function (IMF) were effective features. At the same time the random forest (RF) algorithm was best at identifying trend-features, and the extreme learning machine (ELM) was better at identifying amplitude-features. We proposed a complementary troubleshooting (CT) method for the online identification of construction waste. After using the ELM to identify the characteristic reflectivity, the RF was used to identify first derivative for supplemental verification, which reduced errors due to working conditions and improved the overall model robustness and correctness. The accuracy of proposed method can reach 100% in identifying 180 samples with 6 types including woods, plastics, bricks, concretes, rubbers and black bricks.