We consider R the ring of polynomials in x₁, x₂, ... , x_n with coefficients from an infinite field k, i.e R = k[x₁, x₂, ... , x_n] and the subsets R_d of all polynomials of degree of d. The direct sum R = ⊕_{d ∈ N} R_d is called the degree grading. Let I ⊂ k[x₁, x₂, ... , x_n] be a homogeneous ideal. We define the vector space V_d(I) = R_d ∩ I. If {g₁, ..., g_s} is a basis of I involving only homogeneous polynomials, then V_d(I) is generated by all monomial multiples x₁^α₁x₂^α₂...x_n^α_n g_i with α₁+α₂+ ... + α_n = d.

The known methods for finding a generating set for syzygy module of I involves a Gröbner basis computation. In this study our aim is to find a generating set for syzygy modules using only techniques of linear algebra. This will give us a method for finding H-basis of any polynomial ideal involving only techniques of linear algebra. It is well known that H-bases is more suitable than Gröbner basis in some applications such as solving polynomial systems and interpolation. Hence finding an H-basis without doing whole computtaion of Gröbner basis will be usefull.