diff --git a/.github/build/linux/Dockerfile b/.github/build/linux/Dockerfile
index 2141878d..ff10abe0 100644
--- a/.github/build/linux/Dockerfile
+++ b/.github/build/linux/Dockerfile
@@ -3,14 +3,15 @@ FROM quay.io/pypa/$BASE
 
 ARG UID=1000
 ARG GID=$UID
-ENV PATH="/opt/python/cp36-cp36m/bin:${PATH}"
+# Highest version supported by manylinux1:
+ENV PATH="/opt/python/cp39-cp39/bin:${PATH}"
 
 RUN groupadd -o -g $GID runner && \
     useradd -o -u $UID -g $GID runner && \
     if [[ $AUDITWHEEL_PLAT == manylinux2014_* ]]; then \
         yum install -y glibc-static; \
     fi && \
-    pip install --upgrade cmake cython --only-binary=cmake && \
+    pip install --upgrade cmake 'cython>=3.1.0a1' --only-binary=cmake && \
     for PYBIN in /opt/python/cp3*/bin; do \
         "${PYBIN}/pip" install -U setuptools; \
     done