The gamma-ray binary LS I +61°303 shows a discontinuity of the periodicity in its GeV emission. In this paper, we show that during the epochs when the timing analysis fails to determine the orbital periodicity, the periodicity is in fact present in the two orbital phase intervals $\Phi = 0.0-0.5$ and $\Phi = 0.5-1.0$. That is, there are two periodic signals, one towards periastron (i.e., $\Phi = 0.0-0.5$) and another one towards apastron ($\Phi = 0.5-1.0$). The apastron peak shows the same orbital shift as the radio outburst and, in addition, reveals the same two periods $P_1$ and $P_2$ that are present in the radio data. The gamma-ray emission of the apastron peak normally just broadens the emission of the peak around periastron. Only when it appears at $\Phi = 0.8-1.0$, because of the orbital shift, it is detached enough from the first peak to become recognizable as a second orbital peak, which is the reason why the timing analysis fails. Two gamma-ray peaks along the orbit are predicted by the two-peak accretion model for an eccentric orbit that was proposed by several authors for LS I +61°303.