Spin-polarized scanning tunneling microscopy has been applied to study noncollinear spin textures of a Mn monolayer on a fourfold symmetric W(001) substrate revealing a zero-field spin spiral ground state and two different types of rotational domain walls. With an applied magnetic field of 9 T, we observe a coexistence of the spin spiral and the skyrmion phase, even though a previous theoretical study reported that the phase transition occurs at 18 T. The skyrmions show a roughly hexagonal arrangement despite the square lattice symmetry of the W(001) substrate. Based on a reduced set of energy parameters, we are able to describe the experimental findings and to analyze the topological properties of the rotational domain walls.