NOVELTY - Producing dimethyl ether involves combining methane, water and carbon dioxide under reaction conditions sufficient to form a mixture of hydrogen and carbon monoxide; reacting the hydrogen and carbon dioxide in the mixture to form methanol and steam; separating some or all of the steam produced during the reaction of hydrogen and carbon monoxide; and reacting, in the presence of the steam at least some of which is recycled after being separated, methane and carbon dioxide under reaction conditions sufficient to form dimethyl ether.    USE - For producing dimethyl ether and methanol (claimed), which are useful as synthetic internal combustion engine fuel, diesel fuels, gasoline-methanol mixed fuels; as energy storage and transportation materials to minimize or eliminate the disadvantages or dangers inherent in the use and transportation of liquefied natural gas or liquefied petroleum gas; as household gas to replace natural gas; as raw materials for producing olefins (e.g. ethylene, propylene) synthetic hydrocarbons; and for preparing single cell proteins for human or animal consumption; in the chemical industry e.g. to manufacture a large variety of chemical products and materials, including basic chemicals such as formaldehyde, acetic acid; polymers, paints, adhesives, construction materials; as feedstock for chloromethanes, methylamines, methyl methacrylate, and dimethyl terephthalate; to manufacture products such as resins, antifreeze, and plastics.    ADVANTAGE - The methods converts methane and carbon dioxide and water to dimethyl ether, without any release of carbon dioxide to the atmosphere, without by-product formation or the use of hydrogen to produce water. This provides for significant economical and environmental advantages. Any unreacted starting or intermediate products can be readily recovered and recycled. The process provides for, control, high selectivity and yield of the conversion of carbon dioxide to methanol without any by-products and without encountering the difficulties and having the disadvantages associated with concurrent partial oxidation resulting in undesirable excess carbon dioxide and water. The process also allow for recycling of the water produced from the subsequent dehydration of formed methanol and do not require the use of external water.