Can I change from Z to F then back to Z?

An agency in my country processed my work visa. They charged me a huge sum of money. I got a one year Z in 2011 but my employer disappointed me so I transferred to a new company. However my new employer failed to renew mine so they got me an F instead. I will be back in my country to reapply again for a new Z. Is it possible? Is it the best way to obtain a legitimate one? Please help. Thanks.