Superconductivity (SC) with the suppression of long-range antiferromagnetic (AFM) order is observed in the parent compounds of both iron-based and cuprate superconductors. The AFM wave vectors are bicollinear ($pi$, 0) in the parent compound FeTe different from the collinear AFM order ($pi$, $pi$) in most iron pnictides. Study of the phase diagram of Fe$_{1+y}$Te$_{1-x}$Se$_x$ is the most direct way to investigate the competition between bicollinear AFM and SC. However, presence of interstitial Fe affects both magnetism and SC of Fe$_{1+y}$Te$_{1-x}$Se$_x$, which hinders the establishment of the real phase diagram. Here, we report the comparison of doping-temperature ($x$-$T$) phase diagrams for Fe$_{1+y}$Te$_{1-x}$Se$_x$ (0 $leq$ $x$ $leq$ 0.43) single crystals before and after removing interstitial Fe. Without interstitial Fe, the AFM state survives only for $x$ $<$ 0.05, and bulk SC emerges from $x$ = 0.05, and does not coexist with the AFM state. The previously reported spin glass state, and the coexistence of AFM and SC may be originated from the effect of the interstitial Fe. The phase diagram of Fe$_{1+y}$Te$_{1-x}$Se$_x$ is found to be similar to the case of the 1111 system such as LaFeAsO$_{1-x}$F$_x$, and is different from that of the 122 system.
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