The establishment of a unified earthquake catalog is a basic requirement for attaining a detailed seismological analysis and an improved seismic hazard assessment. Accordingly, the current research paper aims to present a reliable instrumental unified earthquake catalog for the northern part of Algeria. This unified catalog is compiled using regional empirical relationships derived from converting different magnitude scales to an advanced physical-based moment magnitude scale suggested in the recent literature and denoted by Mwg. The regression methodology used in this study is called the New General Orthogonal Regression approach (N.GOR), which was selected since it is the most trustworthy procedure for scaling the magnitudes to Mwg. To highlight the significance of using the N.GOR, the obtained outcomes of the scaling relations were compared with those issued from the conventional general orthogonal regression (GOR) method, which is deemed to be the most dependable methodology used worldwide for magnitude conversion problems. The unified earthquake catalog was assembled from 1954 to 2022. Reliably converting the original magnitudes into homogenized moment magnitude leads to a complete and consistent unified earthquake catalog. Indeed, the unified moment magnitude catalog presented in this paper could provide reliable data for studying earthquakes distribution and the assessment of seismic hazards in the north of Algeria.