This dataset contains the data acquired on the 20 m-long core CAS16-04PC (16°42.380’N, 60°36.907’W, 5706 mbsl) sampled with the Calypso piston coring system in the Désirade Basin offshore the Guadeloupe island (Lesser Antilles) during the research cruise CASEIS (DOI 10.17600/16001800) on board of the R/V Pourquoi Pas?,  between May 28th to July 05th 2016. The core was divided in twelve 150 cm-thick sections and one 110 cm-thick section. This dataset consists of the raw data measured: 1) on board with the GEOTECK Multi Sensor Core Logger of the Quebec University at Rimouski (on the whole core: P-wave velocity, gamma density, and volumetric magnetic susceptibility; and on the split core:  high resolution photographs, surface magnetic susceptibility and spectrophotocolorimetry); and 2) the X-ray images with the SCOPIX system and the semi-quantitative chemical elementary profiles with an AVAATECH XRF core scanner at UMR EPOC Bordeaux. 35 turbidites has been identified, including 3 thick deposits interpreted as homogenite/turbidite (up to 4 m-thick), intercalated with hemipelagic sediment layers.