This letter proposes a secure beamforming design for downlink non-orthogonal multiple access (NOMA) systems utilizing fluid antenna systems (FAS). We consider a setup where a base station (BS) with $M$ fluid antennas (FAs) communicates to a cell-center user (CU) and a cell-edge user (CEU), each with a FA. The CU is the intended recipient while the CEU is regarded as a potential eavesdropper. Our aim is to maximize the achievable secrecy rate by jointly optimizing the secure beamforming vectors and the positions of FAs. To tackle this, we adopt an alternating optimization (AO) algorithm that optimizes secure beamforming and the positions of the FAs iteratively while keeping the other variables fixed. Numerical results illustrate that when FAs meet NOMA, the proposed scheme greatly enhances the secrecy rate compared to conventional multiple-input single-output (MISO) fixed antenna NOMA systems and other benchmark schemes.