A partial wave analysis of the of the $pi ^0pi ^0$ system produced in the charge exchange reaction: $pi ^-pto pi ^0pi ^0n$ at an incident momentum of $18.3 GeV/c$ is presented as a function of ${pi ^0pi ^0}$ invariant mass, $m_{pi^0pi^0}$, and momentum transfer squared, $| {t} |$, from the incident $pi^-$ to the outgoing ${pi ^0pi ^0}$ system.