You can't create hydrogen and oxygen from nothing, as that would violate the law of conservation of mass. However, you can extract hydrogen and oxygen from other sources that don't involve water. Here are some methods:

1. Electrolysis of Other Compounds:

* Electrolysis of Molten Metal Oxides: Certain metal oxides, like lithium oxide (Li₂O), can be electrolyzed in their molten state. This process breaks down the oxide into its constituent elements, producing oxygen gas at the anode and lithium metal at the cathode.

* Electrolysis of Acids: Some acids, like sulfuric acid (H₂SO₄), can be electrolyzed to produce hydrogen gas at the cathode and oxygen gas at the anode. However, this process is less efficient than electrolysis of water and can be more hazardous.

2. Chemical Reactions:

* Thermal Decomposition of Metal Oxides: Certain metal oxides, such as mercuric oxide (HgO), decompose into their elements when heated. Heating HgO releases mercury and oxygen gas.

* Decomposition of Hydrogen Peroxide: Hydrogen peroxide (H₂O₂) can decompose into water and oxygen gas in the presence of a catalyst like manganese dioxide. This process is used in some rocket fuels.

3. Photolysis:

* Photolysis of Water: This method uses light energy to directly break water molecules into hydrogen and oxygen. It's a promising area of research for sustainable energy production.

Note: While these methods can generate hydrogen and oxygen, they are often more complex, costly, and less efficient than using water electrolysis. Water is the most abundant source of hydrogen and oxygen, making it the most practical option for most applications.