PWM Square Wave generator and its complementary

Hello,

I want to generate a square function and its complementary in a range between 20kHz up to 200kHz in Arduino One.

I have tried using the tone function but it is limited to 65kHz. Also, I have not been able to generate a complementary wave which is syncronous with the other (when wave 1 is HIGH, wave 2 is LOW).

I heard that there is a way to generate the complementary wave through the PWM of the microcontroller but I have not found any documentation on how to do it.

Any ideas?

Thanks in advance

Do you want a variable duty cycle or is 50% (as in the tone library) OK ?
Arduino One is the direct English translation from the Italian Arduino Uno ?