Summary: A partial Steiner \((n,k,l)\)-system or briefly \((n,k,l)\)-system is a pair \((V,{\mathbf S})\), where \(V\) is an \(n\)-set and \({\mathbf S}\) is a collection of \(k\)-subsets of \(V\), such that every \(l\)-subset of \(V\) is contained in at most one \(k\)-subset of \({\mathbf S}\). A subset \(X\subset V\) is called independent if \([X]^ k\cap{\mathbf S}=\varnothing\). The size of the largest independent set in \({\mathbf S}\) is denoted by \(\alpha({\mathbf S})\). Define \[ f(n,k,l)=\min\bigl\{\alpha({\mathbf S}),\;{\mathbf S}\text{ is an }(n,k,l)\text{-system}\bigr\}. \] The purpose of this note is to prove that for every \(k\), \(l\), \(k>l\), \[ cn^{{k-l\over k-1}}(\log n)^{{1\over k-1}}\leq f(n,k,l)\leq dn^{{k-l\over k-1}}(\log n)^{{1\over k-1}} \] holds, where \(c\), \(d\) are positive constants depending on \(k\) and \(l\) only.