Yes. The melanin does not change but several other layers do:
The colour of the eye, as defined by the colour of the iris, doesn’t change post-mortem. If a person has brown eyes, this is due to a higher concentration of melanin in the iris than a person with blues eyes (as Fafalone said). However, the colour of the iris is not dependent upon the continual production of melanin. When a person with brown eyes dies, the colour of the iris remains unaffected.
The change in eye colour that you can see in the eyes of dead people is due to opacity of the cornea, aqueous humour and lense brought about by lack of oxygen. Once a person dies, they stop producing tears and blinking, and blood circulation ceases. The cornea must be moist in order that oxygen may be absorbed.
So, the iris of the individual stays whatever colour it was. However, the pupils dilate on death and if you look into the (now very large) pupils a few hours after death, you will notice a distictive blue-white ‘haze’. This is the change that people report.
If you want an example, but want to avoid staring into the eyes of a dead person (which is not very pleasant), look at the eyes of a dead fish. The same thing happens there, and you will see the noticable blue-white colour in the pupil.