Well you cannot really do without leap years, but what you propose looks a lot like the pataphysical calendar: https://en.wikipedia.org/wiki/%27Pataphysics#Pataphysical_ca...

13 months of 29 days. The 29th of each month being imaginary with two exceptions, 1 annual and 1 leap.

Or more seriously, https://en.wikipedia.org/wiki/International_Fixed_Calendar