In the paper \emph{Free biassociative groupoids}, the variety of biassociative groupoids (i.e., groupoids that satisfy the condition: every subgroupoid generated by at most two elements is a subsemigroup) is considered and free objects are constructed using a chain of partial biassociative groupoids that satisfy certain properties. The obtained free objects in this variety are not canonical. By a \textit{canonical groupoid} in a variety $\mathcal{V}$ of groupoids we mean a free groupoid $(R,*)$ in $\mathcal{V}$ with a free basis $B$ such that the carrier $R$ is a subset of the absolutely free groupoid $(T_B,\cdot)$ with the free basis $B$ and $(tu\in R\;\Rightarrow\;t,u\in R\,\,\&\,\,t*u=tu)$. In the present paper, a canonical description of free objects in the variety of biassociative groupoids is obtained.