L293D is very hot to drive this stepper motor, HELP for Final Project

I want to drive a unipolar stepper motor using Arduino and Motor Shield:
Here is the motor driver:

http://www.ladyada.net/make/mshield/

And this is the stepper motor:


The stepper motor consists of 5 pins, 4 to the driver, and 1 to the positive power supply

Then I supply the driver 5V from Arduino Uno microcontroller.
From another power supply I supply +6.5V to Stepper motor, with all the ground connected.

But it results very hot in the L293D IC in the driver, the motor also didnt work well even the coding has been ok.

Is there a way to solve this?
Do I need to replace the driver?
Any suggested driver so I can control the motor using Arduino code?
Is my connection right?

Thank you very much...

The L293D can't safely pass enough current to drive that stepper. A driver based on the L298N should be OK with that stepper, but you would need to use a supply of about 9V because of its voltage drop. If you want to use a 6.5V supply, you need a mosfet-based stepper driver.

EDIT: just noticed it's a unipolar stepper, so the simplest way to drive it is with four logic-level mosfets. Don't forget to connect flyback diodes across the coils.

So if I use L298N driver, could I still use the same library which I use for L293?
If not how to code this motor in arduino ide using L298?
So the solution is I only need to use L298 and that motor, is there any other components?
Is it safe for my microcontroller which connect to the driver as power supply?