Objective: Frequent false alarms from computer-assisted monitoring systems may harm the safety of patients with non-convulsive status epilepticus (NCSE). In this study, we aimed at reducing false alarms in the NCSE detection based on preventing from three common errors: over-interpretation of abnormal background activity, dense short ictal discharges and continuous interictal discharges as ictal discharges. Approach: We analyzed 10 participants' hospital-archived 127-hour electroencephalography (EEG) recordings with 310 ictal discharges. To reduce the false alarms caused by abnormal background activity, we used morphological features extracted by visibility graph methods in addition to time-frequency features. To reduce the false alarms caused by over-interpreting short ictal discharges and interictal discharges, we created two synthetic classes-'Suspected Non-ictal' and 'Suspected Ictal'-based on the misclassified categories and constructed a synthetic 4-class dataset combining the standard two classes-'Non-ictal' and 'Ictal'-to train a 4-class classifier. Precision-recall curves were used to compare our proposed 4-class classification model and the standard 2-class classification model with or without the morphological features in the leave-one-out cross validation stage. The sensitivity and precision were primarily used as performance metrics for the detection of a seizure event. Main results: The 4-class classification model improved the performance of the standard 2-class model, in particular increasing the precision by 15% at an 80% sensitivity level when only time-frequency features were used. Using the morphological features, the 4-class classification model achieved the best performances: a sensitivity of 93% ± 12% and a precision of 55% ± 30% in the group level. 100% accuracy was reached in a participant's 4.3-hour recording with 5 ictal discharges. Significance: False alarms in the NCSE detection were remarkably reduced using the morphological features and the proposed 4-class classification model.