  We study the dissection of a square into congruent convex polygons. Yuan
\emph{et al.} [Dissecting the square into five congruent parts, Discrete Math.
\textbf{339} (2016) 288-298] asked whether, if the number of tiles is a prime
number $\geq 3$, it is true that the tile must be a rectangle.
  We conjecture that the same conclusion still holds even if the number of
tiles is an odd number $\geq 3$.
  Our conjecture has been confirmed for triangles in earlier works. We prove
that the conjecture holds if either the tile is a convex $q$-gon with $q\geq 6$
or it is a right-angle trapezoid.
