The aim of this worksheet is to give an explicit description in term of bases over Z, of some Eichler orders of an indefinite quaternion algebra B defined over Q. Following a work of Hashimoto, we give a procedure which returns a basis of the Eichler orders of level N. This construction provides a very useful tool for working with Eichler orders. Let q be a prime number not dividing the discriminant of B; it is well known that there are two natural inclusions of R(Nq) in R(N). We provide a new procedure in Maple which returns a basis of an Eichler order on level Nq in B and a basis of the other copy of R(Nq) in R(N).