Aims: We provide an open-source code allowing an easy, intuitive, and robust normalisation of spectra. Methods: We developed RASSINE, a Python code for normalising merged 1D spectra through the concepts of convex hulls. The code uses six parameters that can be easily fine-tuned. The code also provides a complete user-friendly interactive interface, including graphical feedback, that helps the user to choose the parameters as easily as possible. To facilitate the normalisation even further, RASSINE can provide a first guess for the parameters that are derived directly from the merged 1D spectrum based on previously performed calibrations. Results: For HARPS spectra of the Sun that were obtained with the HELIOS solar telescope, a continuum accuracy of 0.20% on line depth can be reached after normalisation with RASSINE. This is three times better than with the commonly used method of polynomial fitting. For HARPS spectra of $\alpha$ Cen B, a continuum accuracy of 2.0% is reached. This rather poor accuracy is mainly due to molecular band absorption and the high density of spectral lines in the bluest part of the merged 1D spectrum. When wavelengths shorter than 4500 \AA are excluded, the continuum accuracy improves by up to 1.2%. The line-depth precision on individual spectrum normalisation is estimated to be 0.15%, which can be reduced to the photon-noise limit (0.10%) when a time series of spectra is given as input for RASSINE. Conclusions: With a continuum accuracy higher than the polynomial fitting method and a line-depth precision compatible with photon noise, RASSINE is a tool that can find applications in numerous cases, for example stellar parameter determination, transmission spectroscopy of exoplanet atmospheres, or activity-sensitive line detection.