Memoryless quasi-Newton method is exactly the quasi-Newton method for which the approximation to the inverse of Hessian, at each step, is updated from a positive multiple of identity matrix. Hence its search direction can be computed without the storage of matrices, namely O(n²) storages. In this paper, a memoryless symmetric rank one (SR1) method for solving large-scale unconstrained optimization problems is presented. The basic idea is to incorporate the SR1 update within the framework of the memoryless quasi-Newton method. However, it is well-known that the SR1 update may not preserve positive definiteness even when updated from a positive definite matrix. Therefore, we propose that the memoryless SR1 method is updated from a positive scaled of the identity, in which the scaling factor is derived in such a way to preserve the positive definiteness and improves the condition of the scaled memoryless SR1 update. Under some standard conditions it is shown that the method is globally and R-linearly convergent. Numerical results show that the memoryless SR1 method is very encouraging.