diff --git a/frmts/vrt/vrtdataset.h b/frmts/vrt/vrtdataset.h
index 439f3341f0db..aa6e352b296e 100644
--- a/frmts/vrt/vrtdataset.h
+++ b/frmts/vrt/vrtdataset.h
@@ -909,7 +909,7 @@ class CPL_DLL VRTDerivedRasterBand CPL_NON_FINAL : public VRTSourcedRasterBand
                                    GDALDerivedPixelFuncWithArgs pfnPixelFunc,
                                    const char *pszMetadata);
 
-    static std::pair<PixelFunc, CPLString> *
+    static const std::pair<PixelFunc, std::string> *
     GetPixelFunction(const char *pszFuncNameIn);
 
     void SetPixelFunctionName(const char *pszFuncNameIn);
diff --git a/frmts/vrt/vrtderivedrasterband.cpp b/frmts/vrt/vrtderivedrasterband.cpp
index bfc3d3aca48a..68da4fc18b14 100644
--- a/frmts/vrt/vrtderivedrasterband.cpp
+++ b/frmts/vrt/vrtderivedrasterband.cpp
@@ -50,10 +50,6 @@ using namespace GDALPy;
 #define GDAL_VRT_ENABLE_PYTHON_DEFAULT "TRUSTED_MODULES"
 #endif
 
-static std::map<CPLString,
-                std::pair<VRTDerivedRasterBand::PixelFunc, CPLString>>
-    osMapPixelFunction;
-
 /* Flags for getting buffers */
 #define PyBUF_WRITABLE 0x0001
 #define PyBUF_FORMAT 0x0004
@@ -221,6 +217,20 @@ void VRTDerivedRasterBand::Cleanup()
 {
 }
 
+/************************************************************************/
+/*                      GetGlobalMapPixelFunction()                     */
+/************************************************************************/
+
+static std::map<std::string,
+                std::pair<VRTDerivedRasterBand::PixelFunc, std::string>> &
+GetGlobalMapPixelFunction()
+{
+    static std::map<std::string,
+                    std::pair<VRTDerivedRasterBand::PixelFunc, std::string>>
+        gosMapPixelFunction;
+    return gosMapPixelFunction;
+}
+
 /************************************************************************/
 /*                           AddPixelFunction()                         */
 /************************************************************************/
@@ -251,7 +261,7 @@ CPLErr CPL_STDCALL GDALAddDerivedBandPixelFunc(
         return CE_None;
     }
 
-    osMapPixelFunction[pszName] = {
+    GetGlobalMapPixelFunction()[pszName] = {
         [pfnNewFunction](void **papoSources, int nSources, void *pData,
                          int nBufXSize, int nBufYSize, GDALDataType eSrcType,
                          GDALDataType eBufType, int nPixelSpace, int nLineSpace,
@@ -294,8 +304,8 @@ CPLErr CPL_STDCALL GDALAddDerivedBandPixelFuncWithArgs(
         return CE_None;
     }
 
-    osMapPixelFunction[pszName] = {pfnNewFunction,
-                                   pszMetadata != nullptr ? pszMetadata : ""};
+    GetGlobalMapPixelFunction()[pszName] = {
+        pfnNewFunction, pszMetadata != nullptr ? pszMetadata : ""};
 
     return CE_None;
 }
@@ -343,7 +353,7 @@ CPLErr VRTDerivedRasterBand::AddPixelFunction(
  * @return A derived band pixel function, or NULL if none have been
  * registered for pszFuncName.
  */
-std::pair<VRTDerivedRasterBand::PixelFunc, CPLString> *
+const std::pair<VRTDerivedRasterBand::PixelFunc, std::string> *
 VRTDerivedRasterBand::GetPixelFunction(const char *pszFuncNameIn)
 {
     if (pszFuncNameIn == nullptr || pszFuncNameIn[0] == '\0')
@@ -351,9 +361,10 @@ VRTDerivedRasterBand::GetPixelFunction(const char *pszFuncNameIn)
         return nullptr;
     }
 
-    auto oIter = osMapPixelFunction.find(pszFuncNameIn);
+    const auto &oMapPixelFunction = GetGlobalMapPixelFunction();
+    const auto oIter = oMapPixelFunction.find(pszFuncNameIn);
 
-    if (oIter == osMapPixelFunction.end())
+    if (oIter == oMapPixelFunction.end())
         return nullptr;
 
     return &(oIter->second);
@@ -935,7 +946,7 @@ CPLErr VRTDerivedRasterBand::IRasterIO(
     }
 
     /* ---- Get pixel function for band ---- */
-    std::pair<PixelFunc, CPLString> *poPixelFunc = nullptr;
+    const std::pair<PixelFunc, std::string> *poPixelFunc = nullptr;
     std::vector<std::pair<CPLString, CPLString>> oAdditionalArgs;
 
     if (EQUAL(m_poPrivate->m_osLanguage, "C"))