If you have a bike of over 250 cc your chain is probably of the 'endless' type, this means that it was fitted then a special link was rivited closed in situ, making the chain effectivly one complete circle. You can split this link, as you will have to do when you replace the chain when it is worn out, but you will not then be able to replace it. You will need a special tool, called not surprisingly a chain splitter(!), to do this. Failing that you can remove a link by grinding off the heads of the rivets with an angle grinder, again though, the chain will then be shot. Smaller bikes with less powerful engines usually have a chain with a link that has a spring loaded clip keeping it closed, this can be removed and replaced. In any case, im not sure that cleaning the thing is your problem. Unless you ride off road, or regularly in bad conditions, you should not need to clean it very often, as it is getting rusty it suggests to me that you are cleaning off the lubricant, a chain is supposed to look a bit oily and messy, that is good! What chain lube are you using? Castrol chain wax will leave a film of greasy residue on the chain that will stop it going rusty, and it will not fly off as you ride. I have used it for years and find it to be good. A good spray of 3in1 oil will also work into the links and will resist water and rust, and will not harm the o-rings, although of course it will evaporate and excess will fly off so you will have to re-do it every month or so in winter.