Abstract: The solar wind turbulence is now widely believed as describable by a critical balance cascade based on -2 scaling index measured in the direction parallel to the local magnetic field reported by many papers. However, previous studies have shown that both wavelet analyses and structure function analyses may be influenced by the intermittency and structures in the solar wind. One way to reliably obtain the true spectral index is to remove the intermittency and structures and another way is to put strict criteria on the parallel selection. Previous results show that the parallel scaling index is around −5/3 after removing intermittency or under strict criteria for low-amplitude fluctuations. Here we present results of the scaling with precise local magnetic field directions. We first select the parallel observations with a small (<10^o) θ_VB (the angle between the average of two-time-instant magnetic field ( B _l) and the average of the same two-time-instant velocity). We define precise parallel direction as the parallel observations with a small (<10^o) ϕ (the angle between B _l and another local magnetic field B ₀ determined as the average of the time series observed between the corresponding two time instants.) The precise perpendicular direction is defined in a similar way. The condition whether or not B _l and B ₀ are parallel could help to determine the precise magnetic direction. The lower ϕ, the more precise the direction is. We find that the scaling index of the magnetic-trace structure function is strongly affected by the value of ϕ. As ϕ decreases, in other words, the preciseness of direction increases, the anisotropy gradually weakens and eventually almost disappears. This could be due to the fact that there are more structures at the larger scale and constraining ϕ to a low value leads to more power removed at the larger scale. This effect causes the change of the scaling index: the steep parallel index becomes flatter, especially in the parallel direction. We find that the scaling index of the magnetic (velocity)-trace structure functions are −0.67±0.11 (−0.55±0.18) and −0.55±0.10 (−0.46±0.09) respectively in the precise parallel and perpendicular directions. These new results are not consistent with the −2 scaling index and may not favor the application of the critical balance framework in the solar wind fluctuations. The fluctuation amplitudes of the magnetic field and the velocity are both moderate, which expands the determination of isotropy from the low-amplitude condition in previous work to the moderate-amplitude condition. Our results help to distinguish the true feature of the scaling index anisotropy in the solar wind and will initiate new theoretical study on solar wind turbulence.