Automatic seizure detection leveraging artificial intelligence has gained widespread attention. However, existing research has predominantly focused on scenarios with patient-specific and fixed-time lengths, with the practical clinical applications across non-specific patients and variable time lengths remaining underexplored. To address this gap, we introduce a novel method named Electroencephalogram Channel-wise Normalization (ECNorm), designed to thoroughly explore the physical significance and data distribution characteristics of different EEG channels to minimize inter-patient variability. We applied ECNorm to a two-layer LSTM model to facilitate cross-patient adaptive-length epilepsy diagnosis. Ablation studies demonstrate that ECNorm significantly enhances the performance of simple architectures like the two-layer LSTM when compared to batch normalization and layer normalization. Leave-one-out experiments on the public CHB-MIT dataset verify that our approach surpasses existing studies across segments of varying lengths (1 and 100 seconds), establishing a new benchmark for patient-independent automated epilepsy diagnosis.