The all-sky 408 MHz map of Haslam et al. is one the most important total-power radio surveys. It has been widely used to study diffuse synchrotron radiation from our Galaxy and as a template to remove foregrounds in cosmic microwave background data. However, there are a number of issues associated with it that must be dealt with, including large-scale striations and contamination from extragalactic radio sources. We have re-evaluated and reprocessed the rawest data available to produce a new and improved 408-MHz all-sky map. We first quantify the positional accuracy (≈7 arcmin) and effective beam (56.0 ± 1.0 arcmin) of the four individual surveys from which it was assembled. Large-scale striations associated with 1/f noise in the scan direction are reduced to a level ≪1 K using a Fourier-based filtering technique. The most important improvement results from the removal of extragalactic sources. We have used an iterative combination of two techniques – two-dimensional Gaussian fitting and minimum curvature spline surface inpainting – to remove the brightest sources (≳2 Jy), which provides a significant improvement over previous versions of the map. We quantify the impact with power spectra and a template fitting analysis of foregrounds to the WMAP data. The new map is publicly available and is recommended as the template of choice for large-scale diffuse Galactic synchrotron emission. We also provide a higher resolution map with small-scale fluctuations added, assuming a power-law angular power spectrum down to the pixel scale (1.7 arcmin). This should prove useful in simulations used for studying the feasibility of detecting H i fluctuations from the Epoch of Reionization.