Schizophrenia is a chronic mental disorder that affects millions of people around the world. Neurologists commonly use EEG signals to distinguish schizophrenia patients from normal controls, but their manual analysis is tedious and time-consuming. This has motivated the need for automated methods based on machine learning. However, the methods based on hand-engineered features need human experts to decide which features should be extracted. Though deep learning has recently shown good results for schizophrenia detection, the existing deep models have high parameter complexity, making them prone to overfitting because the available data are limited. To overcome these limitations, we propose a method based on an ensemble-like approach and a lightweight one-dimensional convolutional neural network to discriminate schizophrenia patients from healthy controls. It splits an input EEG signal for analysis into smaller segments, where the same backbone model analyses each segment. In this way, it makes decisions after scanning an EEG signal of any length without increasing the complexity; i.e., it scales well with an EEG signal of any length. The model architecture is simple and involves a small number of parameters, making it easy to implement and train using a limited amount of data. Though the model is lightweight, enough trials are still needed to learn the discriminative features from available data. To tackle this issue, we introduce a simple data augmentation scheme. The proposed method achieved an accuracy of 99.88% on a public benchmark dataset; it outperformed the state-of-the-art methods. It will help neurologists in the rapid and accurate detection of schizophrenia patients.