The Milankovitch theory states that global climate variability on orbital timescales from tens to hundreds of thousands of years is dominated by the summer insolation at high northern latitudes. The supporting evidence includes reconstructed air temperatures in Antarctica that are nearly in phase with boreal summer insolation and out of phase with local summer insolation. Antarctic climate is therefore thought to be driven by northern summer insolation. A clear mechanism that links the two hemispheres on orbital timescales is, however, missing. We propose that key Antarctic temperature records derived from ice cores are biased towards austral winter because of a seasonal cycle in snow accumulation. Using present-day estimates of this bias in the 'recorder' system, here we show that the local insolation can explain the orbital component of the temperature record without having to invoke a link to the Northern Hemisphere. Therefore, the Antarctic ice-core-derived temperature record, one of the best-dated records of the late Pleistocene temperature evolution, cannot be used to support or contradict the Milankovitch hypothesis that global climate changes are driven by Northern Hemisphere summer insolation variations.