Process for dehydrating an alcohol to prepare corresponding olefin(s), comprising: (a) providing a feed comprising at least an alcohol having at least 2 carbon atoms, and preferably at most 5 carbon atoms, or a mixture thereof optionally water, optionally an inert component, in a dehydration unit, (b) placing the feed into contact with an acidic catalyst in a reaction zone of said dehydration unit containing metallic sites at conditions effective to dehydrate at least a portion of the alcohol to make an olefin or a mixture of olefins having the same number of carbon atoms as the alcohol, (c) recovering from said dehydration unit an effluent comprising: - an olefin or a mixture of olefins, - water, - undesired by-products including aldehydes and light products, comprising H 2, CO, CO 2, CH 4, - optionally unconverted alcohol(s) if any, - optionally the inert component, wherein, said feed -providing step (a) being further characterized in that an effective amount of one or more sulphur containing compound capable to reduce the undesired by-products produced by the reforming secondary reaction of said alcohol over said metallic sites by comparison with a non introduction of such sulphur containing compound is added to said feed at step (a) at a sulphur weight concentration of at least 0.5 wt ppm preferably at least 1 wt ppm more preferably at least 2 wt ppm and at most 20 wt ppm preferably at most 10 wt ppm and more preferably at most 5 wt ppm of the total content of said feed with said sulphur containing compound and wherein said acidic catalyst is at least one compound selected from the group consisting of: A crystalline silicate zeolite having a ratio Si/AI higher than 10, A dealuminated crystalline silicate zeolite, A phosphorous modified zeolite, silica-alumina, alumina, silicated, titanated, zirconated or fluorinated alumina silico-aluminophosphates, or a modified crystalline aluminosilicate of the Framework Type FER having Si/AI framework molar ratio greater than 20 and a ratio between strong acid sites and weak acid sites, S/W, lower than 1.0, the ratio S/W being measured by temperature-programmed desorption of ammonia and being determined by the ratio of the peak area of ammonia desorbed above 340°C to that desorbed below 340°C, or any of above cited acidic catalyst, which was subjected to a preliminary pre-coking step. (a) providing a feed comprising at least an alcohol having at least 2 carbon atoms, and preferably at most 5 carbon atoms, or a mixture thereof optionally water, optionally an inert component, in a dehydration unit, (b) placing the feed into contact with an acidic catalyst in a reaction zone of said dehydration unit containing metallic sites at conditions effective to dehydrate at least a portion of the alcohol to make an olefin or a mixture of olefins having the same number of carbon atoms as the alcohol, (c) recovering from said dehydration unit an effluent comprising: - an olefin or a mixture of olefins, - water, - undesired by-products including aldehydes and light products, comprising H 2, CO, CO 2, CH 4, - optionally unconverted alcohol(s) if any, - optionally the inert component, wherein, said feed -providing step (a) being further characterized in that an effective amount of one or more sulphur containing compound capable to reduce the undesired by-products produced by the reforming secondary reaction of said alcohol over said metallic sites by comparison with a non introduction of such sulphur containing compound is added to said feed at step (a) at a sulphur weight concentration of at least 0.5 wt ppm preferably at least 1 wt ppm more preferably at least 2 wt ppm and at most 20 wt ppm preferably at most 10 wt ppm and more preferably at most 5 wt ppm of the total content of said feed with said sulphur containing compound and wherein said acidic catalyst is at least one compound selected from the group consisting of: A crystalline silicate zeolite having a ratio Si/AI higher than 10, A dealuminated crystalline silicate zeolite, A phosphorous modified zeolite, silica-alumina, alumina, silicated, titanated, zirconated or fluorinated alumina silico-aluminophosphates, or a modified crystalline aluminosilicate of the Framework Type FER having Si/AI framework molar ratio greater than 20 and a ratio between strong acid sites and weak acid sites, S/W, lower than 1.0, the ratio S/W being measured by temperature-programmed desorption of ammonia and being determined by the ratio of the peak area of ammonia desorbed above 340°C to that desorbed below 340°C, or any of above cited acidic catalyst, which was subjected to a preliminary pre-coking step. - an olefin or a mixture of olefins, - water, - undesired by-products including aldehydes and light products, comprising H 2, CO, CO 2, CH 4, - optionally unconverted alcohol(s) if any, - optionally the inert component, A crystalline silicate zeolite having a ratio Si/AI higher than 10, A dealuminated crystalline silicate zeolite, A phosphorous modified zeolite, silica-alumina, alumina, silicated, titanated, zirconated or fluorinated alumina silico-aluminophosphates, or a modified crystalline aluminosilicate of the Framework Type FER having Si/AI framework molar ratio greater than 20 and a ratio between strong acid sites and weak acid sites, S/W, lower than 1.0, the ratio S/W being measured by temperature-programmed desorption of ammonia and being determined by the ratio of the peak area of ammonia desorbed above 340°C to that desorbed below 340°C,