diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index f630115..98bf870 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -65,6 +65,7 @@ jobs:
         uses: ./
         with:
           method: ${{matrix.method}}
+          log-file-suffix: '${{matrix.method}}-${{matrix.os}}'
 
       - name: Run the action on this runner with nvcc and libcublas subpackages (Linux)
         if: runner.os == 'Linux' && matrix.method == 'network'
@@ -73,7 +74,7 @@ jobs:
           method: ${{matrix.method}}
           sub-packages: '["nvcc"]'
           non-cuda-sub-packages: '["libcublas"]'
-          log-file-suffix: 'nvcc-libcublas'
+          log-file-suffix: 'nvcc-libcublas-${{matrix.method}}-${{matrix.os}}'
 
       - name: Run the action on this runner with nvcc subpackage only (Windows)
         if: runner.os == 'Windows'
@@ -81,7 +82,7 @@ jobs:
         with:
           method: ${{matrix.method}}
           sub-packages: '["nvcc"]'
-          log-file-suffix: 'nvcc'
+          log-file-suffix: 'nvcc-${{matrix.method}}-${{matrix.os}}'
 
       - name: Test if nvcc is available
         run: nvcc -V
diff --git a/README.md b/README.md
index d199a93..d59a068 100644
--- a/README.md
+++ b/README.md
@@ -48,6 +48,31 @@ See the [Nvidia Docs](https://docs.nvidia.com/cuda/cuda-installation-guide-linux
 
 Default: `'["--toolkit", "--samples"]'`.
 
+### `log-file-suffix`
+
+**Required with matrix builds**
+
+Add suffix to the log file name which gets uploaded as an artifact. This **has** to be set when running a matrix build.
+The log file already contains the OS type (Linux/Windows) and install method (local/network) but it is not aware of other matrix variables, so add those here.
+
+For example if you use multiple linux distros:
+```
+jobs:
+  CI:
+    strategy:
+      matrix:
+        os: [ubuntu-22.04, ubuntu-20.04]
+    runs-on: ${{ matrix.os }}
+    steps:
+    - uses: Jimver/cuda-toolkit@master
+      id: cuda-toolkit
+      with:
+        log-file-suffix: '${{matrix.os}}.txt'
+
+```
+
+Default: `'log.txt'`
+
 ## Outputs
 
 ### `cuda`