We consider R the ring of polynomials in x1, x2, ... , xn with coefficients from an infinite field k, i.e R = k[x1, x2, ... , xn] and the subsets Rd of all polynomials of degree of d. The direct sum R = ⊕d ∈ N Rd is called the degree grading. Let I ⊂ k[x1, x2, ... , xn] be a homogeneous ideal. We define the vector space Vd(I) = Rd ∩ I. If {g1, ..., gs} is a basis of I involving only homogeneous polynomials, then Vd(I) is generated by all monomial multiples x1α1x2α2...xnαn gi with α1+α2+ ... + αn = 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.