Class five technology. Toilet does not completely flush. It appears the flapper drops down too quickly.

Could be low water level in the reservoir, otherwise the flapper may be shutting to quickly to allow enough water to properly flush. You could try holding the flapper open or watch it's operation as you flush the toilet to see if it's allowing enough water to drain into the toilet. It's pretty easy to replace the flapper on most toilets and cheap as well.

The flapper at the bottom of the tank is leaking and needs replacement.

Fill the breather hole (1/8" hole) inside the flapper.This is designed to let air out so the flapper will sink. Now it floats longer letting in more water. 25%percent more in my case.

Try replacing the rubber flapper inside the tank.

The flapper on these toilets is a water saver. The water saver flappers can be replaced with a standard flapper and I have found this will help considerably. The flapper is located in the tank at the center bottom. It is the part that flaps up and down when you pull the lever.

If there is a continual leak in to the toilet bowl you will likely need to replace the flush valve or the toilet flapper.

As a first step try try cleaning the sealing surface of the flush valve to se if the flapper will seat and make a seal.

If this does not work and the flapper is visibly detioriated and breaking down shut off the water supply, remove the toilet flapper and visit your local plumbing supply store to purchase a suitable replacement. Install the new flapper, turn on water supply.

These illustrated instruictions may also assist:

http://www.danco.com/HowTo/How-To-Replace-a-Toilet-Flapper

Although less likely, if the sealing surface of the flush valve is damaged or detioriated proceed with replacement of the flush valve. Again turn off water supply and follow the instructions set out here:

http://www.danco.com/HowTo/How-To-Replace-a-Flush-Valve

If there is not a leak in to the toilet bowl and the water flow does not shut off completely, then water is flowing through the fill valve and the overflow pipe and you may need to adjust the float and float rod to allow clsoure of the fill valve. See here:

http://www.danco.com/HowTo/How-To-Replace-a-Float-and-Float-Rod

what happens is the float is not staying open for long enough, by shorting the chain that goes to the flapper might help but you can only shorten it so much or the flapper does not close all the way then the toilet is just running and running. No you don't want that so the other thing you can do that might work is when you go to flush the toilet just hold the handel down for 5 seconds this will keep the float up and open for the Right amount of time. Other wise the other way to fix it witch is a old school trick is that you need to find a nice small piece of foam, witch floats and is about the size of a old half dollar and as least half inch thick, you place that on the chain that goes to the flapper so when the toilet is flushed the flapper will float and stay open . IF you do this just make sure to use a good piece of foam and secure it properly where it wont come off the chain.

Place a few drops of food coloring in the tank of the toilet, if it is leaking you will see the color seep into the toilet bowl within a short period of time. If you see the food color in the toilet bowl you will need to replace the flapper.

sometimes if you change the flapper and add more water to the tank by adjusting the fill valve they will flush with more power

These models need to have a flush valve flapper that has a styrofoam float on the lift chaninof the flapper. Go to hardware store or home improvement store and get a 'Korky brand toilet tank flapper with float 'ball". Cut the rubber ring piece away from the flapper and you don't need it (see cut here marks on flapper). Install flapper and adjust the float fairly close to the flapper.
When the water level drops in the tank and reaches the level of the float on the opne flapper, the flapper quickly closes causing the toilet to have a "surge" of siphon action which forces the water in the bowl to be drawn out.