Recommender systems play an important role in e-commerce websites as they improve the customer journey by helping the users find what they want at the right moment. In this paper, we focus on identifying a complementary relationship between the products of an e-commerce company. We propose a content-based recommender system for detecting complementary products, using Siamese Neural Networks (SNN). To this end, we implement and compare two different models: Siamese Convolutional Neural Network (CNN) and Siamese Long Short-Term Memory (LSTM). Moreover, we propose an extension of the SNN approach to handling millions of products in a matter of seconds, and we reduce the training time complexity by half. In the experiments, we show that Siamese LSTM can predict complementary products with an accuracy of ~85% using only the product titles.