diff --git a/easystacks/software.eessi.io/2023.06/rebuilds/20241017-eb-4.9.4-OpenBLAS-aarch64-generic.yml b/easystacks/software.eessi.io/2023.06/rebuilds/20241017-eb-4.9.4-OpenBLAS-aarch64-generic.yml
new file mode 100644
index 0000000000..4ba7983da6
--- /dev/null
+++ b/easystacks/software.eessi.io/2023.06/rebuilds/20241017-eb-4.9.4-OpenBLAS-aarch64-generic.yml
@@ -0,0 +1,9 @@
+# 2024.10.17
+# TARGET=ARMV8 must be used when building OpenBLAS for aarch64/generic,
+# since otherwise "Illegal instruction" errors may happen in the driver part of OpenBLAS
+# on systems that only support a minimal instruction set like Arm v8 (like Raspberry Pi SBCs);
+# see also https://github.com/OpenMathLib/OpenBLAS/issues/4945
+easyconfigs:
+  - OpenBLAS-0.3.21-GCC-12.2.0.eb
+  - OpenBLAS-0.3.23-GCC-12.3.0.eb
+  - OpenBLAS-0.3.24-GCC-13.2.0.eb
diff --git a/eb_hooks.py b/eb_hooks.py
index 33bdf53c52..ba6f9ad5da 100644
--- a/eb_hooks.py
+++ b/eb_hooks.py
@@ -491,11 +491,19 @@ def pre_configure_hook_openblas_optarch_generic(self, *args, **kwargs):
             for step in ('build', 'test', 'install'):
                 self.cfg.update(f'{step}opts', "DYNAMIC_ARCH=1")
 
-            # use -mtune=generic rather than -mcpu=generic in $CFLAGS on aarch64,
-            # because -mcpu=generic implies a particular -march=armv* which clashes with those used by OpenBLAS
-            # when building with DYNAMIC_ARCH=1
             if get_cpu_architecture() == AARCH64:
+                # when building for aarch64/generic, we also need to set TARGET=ARMV8 to make sure
+                # that the driver parts of OpenBLAS are compiled generically;
+                # see also https://github.com/OpenMathLib/OpenBLAS/issues/4945
+                for step in ('build', 'test', 'install'):
+                    self.cfg.update(f'{step}opts', "TARGET=ARMV8")
+
+                # use -mtune=generic rather than -mcpu=generic in $CFLAGS for aarch64/generic,
+                # because -mcpu=generic implies a particular -march=armv* which clashes with those used by OpenBLAS
+                # when building with DYNAMIC_ARCH=1
                 cflags = os.getenv('CFLAGS').replace('-mcpu=generic', '-mtune=generic')
+                self.log.info("Replaced -mcpu=generic with -mtune=generic in $CFLAGS")
+                self.log.info("Updating $CFLAGS to: %s", cflags)
                 env.setvar('CFLAGS', cflags)
     else:
         raise EasyBuildError("OpenBLAS-specific hook triggered for non-OpenBLAS easyconfig?!")