This study analyzes the interconnection of the stability of prominent stablecoins including Tether (USDT), USD Coin (USDC), Paxos Standard (PAX), TrueUSD (TUSD) and DAI from 23/11/2019 to 1/04/2021. We find (i) market price fluctuations vary across stablecoins, (ii) instabilities in USDT and USDC significantly drive those of other stablecoins but less convincing evidence for the reverse impact, and (iii) that increases (decreases) in USDT market prices significantly depress (raise) the market prices of the other stablecoins. Interestingly, the algorithmic stablecoin, DAI, is found to be less stable than its USD-backed counterparts.