Read this tutorial:
http://pdp11.byethost12.com/AVR/ArduinoAsProgrammer.htm
Just replace the atmega328p given as an example with your atmega16 and make these connections (supposing that you have an atmega16 in DIL40 package):
Arduino Uno -> pin Atmega16
SS -> 9
MOSI -> 6
MISO -> 7
SCK -> 8