Detecting geomagnetic anomalies preceding earthquakes is a challenging yet promising area of research that has gained increasing attention in recent years. This study introduces a novel reconstruction-based modeling approach enhanced by negative learning, employing a Bidirectional Long Short-Term Memory (BiLSTM) network explicitly trained to accurately reconstruct non-seismic geomagnetic signals while intentionally amplifying reconstruction errors for seismic signals. By penalizing the model for accurately reconstructing seismic anomalies, the negative learning approach effectively magnifies the differences between normal and anomalous data. This strategic differentiation enhances the sensitivity of the BiLSTM network, enabling improved detection of subtle geomagnetic anomalies that may serve as earthquake precursors. Experimental validation clearly demonstrated statistically significant higher reconstruction errors for seismic signals compared to non-seismic signals, confirmed through the Mann-Whitney U test with a p-value of 0.0035 for Root Mean Square Error (RMSE). These results provide compelling evidence of the enhanced anomaly detection capability achieved through negative learning. Unlike traditional classification-based methods, negative learning explicitly encourages sensitivity to subtle precursor signals embedded within complex geomagnetic data, establishing a robust basis for further development of reliable earthquake prediction methods.