It is possible, remember that there are two different "beneficial" bacterias in a cycle tank. The ones that convert ammonia to nitrite, and the ones that convert nitrite to nitrate.
Sounds to me that your tank is close to complete the cycle, meaning that you will soon start to read 0 Nitrites, but in the mean time, you need to keep up with the PWC
as needed. Don't forget not to clean the filter or media during the water changes, do just a light rinse in tank water.